Time transfer and position determination during simultaneous radar and communications operation

ABSTRACT

A system and a method that enable time transfer and position determination services during operation of a combined radar/communications system. One aspect of the method is broadcasting a signal that any system receiving it can use to synchronize system clocks to the set of master clocks among a selected subset of transmitting platforms. This broadcast signal can occur during both radar and communications operations. In addition, with three or more mobile or fixed platforms broadcasting the signal, any one receiving the signal can also derive position information. The time transfer and position determination service can operate at the same time as operation of both radar and communications functions. The broadcast information is derived from internal time and position information as determined by the individual transmitting platforms. A small set of such platforms are configured to broadcast signals that transfer both accurate time and accurate position to all other platforms within radiofrequency (RF) range.

BACKGROUND

The technology disclosed herein generally relates to systems and methodsfor performing combined radar and communications functions. Thetechnology disclosed herein also relates to systems and methods forpositioning, navigation and timing and to distributive collaborativeradar systems.

The Global Positioning System (GPS) is a satellite-based radionavigation system that provides geolocation and time information to aGPS receiver anywhere on or near the Earth where there is anunobstructed line of sight to four or more GPS satellites. Many sectorsof the U.S. economy (such as telecommunications, energy, finance andtransportation) rely on GPS for positioning, navigation and timing.However, GPS can fail, which failure can have detrimental consequences.Concern for the country's reliance on GPS has been growing amongindustry and government workers for many years, especially as thedependency on GPS has grown across industries. This has led to a numberof industries (commercial and military) being highly vulnerable to anyGPS failure.

Three approaches are typically used to mitigate GPS failure. The firstis to interoperate with other global navigation satellite systems.However, these are also subject to the same failure mechanisms as GPS(such as space weather) and are controlled by other governments. Thesecond approach is for everyone to use better clocks. For example,chip-scale atomic clocks the size of a penny are a promising newtechnology that can hold time for about a day, but are currently tooexpensive to deploy widely. Also, long-term synchronization is oftenstill required. The third approach is to use ground-based timing andposition signals such as the eLORAN system, but this system is onlyavailable in limited locations.

It would be desirable to provide a system and a method that solves theproblem of determining time and position information in aradionavigation system without the use of a satellite-based positioningsystem. Previous solutions required separate time transfer and positiondetermination hardware for operation during GPS outages on allplatforms. These solutions also must use separate signaling frequenciesand/or times for such operation. In particular, it would be desirable toenable time transfer and position determination services duringoperation of a combined radar and communications system (hereinafter“combined radar/communications system”).

Distributive collaborative radar systems use cooperating platforms ornodes that operate together to solve a much more complex problem thanindividual radar systems could accomplish operating independently. Forexample, current weather radar systems are fundamentally constrained insensitivity, resolution, and lower atmosphere coverage and lack thecapability to trace and track the storm cells in an adaptive and dynamicmanner, especially for small-scale, high-impact events such astornadoes. By using distributed collaborative adaptive sensing networks,these constraints can be overcome. In particular, a large number ofsmall radar systems can address these limitations, provided that theindividual radar systems are able to collaborate in their sensing ofweather events.

For another example, current distributed radar systems, includingstatistical multi-input multi-output (MIMO) and passive radar systems,have potential capabilities to enhance detection, targetcharacterization and area coverage. (MIMO radar systems transmitmutually orthogonal signals from multiple transmit antennas, and thesewaveforms are extracted from each of multiple receive antennas by a setof matched filters.) In one canonical example, networks of multipledistributed radar sensors can be utilized to survey a large area andobserve targets from a number of different angles. In addition tospatial diversity, other problems such as fluctuating targets and blindspeed problems can also be addressed.

The above-described performance advantages come with attendantissues—such as hardware cost, resource management and algorithmdesign—that need to be resolved in order to make such distributed radarsystems practical. Moreover, if standard waveforms were used forsimultaneous dispersed multiplatform FMCW radar, the interferencebetween platforms would be unacceptably high. Existing solutions requireoperating on different radiofrequency (RF) bands if the platforms arewithin range of each other's sidelobe transmissions or ground bouncereturns. Also, previous solutions do not allow simultaneous dispersedmultiplatform FMCW radar operation as well as simultaneous radar andcommunications using the same waveform.

SUMMARY

The subject matter disclosed in detail below is directed to a system anda method that enable time transfer and position determination servicesduring operation of a combined radar/communications system. In thecombined radar/communications system, a single waveform is used toachieve both efficient radar and efficient communications functions.This waveform will be referred to in this disclosure as a combinedradar/communications waveform (CRCW) and is based on afrequency-modulated continuous waveform (FMCW). This CRCW is part of acombined radar/communications function that can be implemented using acommon antenna, common power and common location on a ground vehicle, anaircraft, a satellite, a submarine or other mobile platform to provideboth types of functions.

The technology proposed herein allows the broadcasting of a CRCW signalthat any system receiving it can use to synchronize system clocks to theset of master clocks among a selected subset of transmitting platforms.This broadcast signal can occur during both radar and communicationsoperations. In addition, with three or more mobile or fixed platformsbroadcasting the signal, any one receiving the signal can also deriveposition information without the use of standard satellite positioningsystems. The system includes hardware configured to perform both radarand communications functions, which enables usage of common antennas,common power and common space on size-, weight- and power-constrainedplatforms such as ground vehicles, aircraft, satellites, submarines andother mobile platforms.

The system includes transmitting platforms of the above-described typewhich further include means for providing time transfer and positiondetermination service to every receiver in the network. The timetransfer and position determination service can operate at the same timeas operation of both radar and communications functions. The broadcastinformation is derived from internal time and position information asdetermined by the individual transmitting platforms. These transmittingplatforms are equipped with high-quality clocks and navigation systemsand serve as the source for correct time and position for all otherplatforms within their communications area. In particular, the time andposition information is added to a communications signal duringsimultaneous radar and communications operations to support anyoperational arena when the system is enabled. This will allow a smallset of such enabled platforms to transfer both accurate time andaccurate position to all other platforms within radiofrequency (RF)range. Note that adding timing and position information applies tocombined radar and communications systems with either fixed or steerableantennas. (For example, the antennas may be phased-array antennas whichare steerable electronically using beamforming.) The time transfer andposition determination service disclosed herein can operate at muchlower signal-to-noise levels (i.e., at much greater ranges) than thecommunications functions. Platforms can easily join or leave the timingand position network due to operation on different frequencies. Furtherimprovements in signal coverage can be achieved by an addition to thebasic system which applies angle jitter to the beams in order toincrease the range of the timing and position broadcasts (referred tohereinafter as “intentional beam jitter”).

Although various embodiments of systems and methods for enabling timetransfer and position determination in a combined radar/communicationssystem will be described in some detail below, one or more of thoseembodiments may be characterized by one or more of the followingaspects.

One aspect of the subject matter disclosed in some detail below is acombined radar/communications system comprising a commonradar/communications transmitter having a transmission antenna and acombined radar and communications receiver having a common receptionantenna, wherein the common radar/communications transmitter isconfigured to transmit frequency-modulated continuous-wave signalsrepresenting packets of data, the data in each packet including payloadsections made up of multiple symbols and timing header/positionprediction slots made up of multiple supersymbols, wherein the payloadsections and timing header/position prediction slots alternate insequence within the packet, and each timing header/position predictionslot includes a respective timing header and a respective positionprediction section which is contiguous with the respective timingheader. Each symbol consists of an up chirp and a down chirp, and eachsupersymbol consists of a concatenation of pairs of up chirps and downchirps of equal chirp lengths, the up chirps of the concatenation havingthe same up phase and the down chirps of the concatenation having thesame down phase. The supersymbols in timing headers of the timingheader/position prediction slots are phase encoded with time informationindicating a duration of time for which a prediction of the position ofthe combined radar/communications system was valid; and the supersymbolsin position prediction sections of the timing header/position predictionslots are phase encoded with position information indicating theprediction of the position of the combined radar/communications system.

In accordance with one embodiment of the combined radar/communicationssystem described in the immediately preceding paragraph, the up and downphases of the supersymbols in each position prediction section in apacket are varied from one position prediction section to a nextposition prediction section to represent respective position predictionsfor the combined radar/communications system which were valid forrespective durations of the respective contiguous timing headers. The upand down phases of the supersymbols in each timing header in a packetare varied from one timing header to a next timing header to representthe respective durations of time for which the respective positionpredictions were valid. A position prediction is associated with atiming header in each timing header/position prediction slot, thecombined information providing a predicted position of the combinedradar/communications system which was valid for the duration of thetiming header transmission.

In accordance with some embodiments, the combined radar/communicationssystem further comprises: a beam steering controller configured tocontrol a direction in which the transmission antenna transmits signalsin response to receipt of a command representing a steering angle; and abeam jitter system configured to generate the command by summing asignal representing a jitter angle to a signal representing a commandedsteering angle. The beam jitter system is further configured to generatesuccessive commands by summing respective signals representingrespective jitter angles of a jitter angle sequence to the signalrepresenting the commanded steering angle.

In accordance with some embodiments, the combined radar/communicationssystem further comprises: a timing correlation module which isconfigured to extract timing information from respective timing headersin packets received from at least three transmitting platforms usingcorrelation; a position demodulation module which is configured toextract position information from respective position predictions in thepackets received from the at least three transmitting platforms usingdemodulation; and a time and position calculation module which isconfigured to compute the local position and time offset of the combinedradar/communications system using the timing and position informationreceived from the at least three transmitting platforms. The localposition data is included in the packet of data transmitted by thecommon radar/communications transmitter. The time offset is used toadjust a local clock.

Another aspect of the subject matter disclosed in some detail below is amethod for determining a position of a mobile platform, comprising:receiving timing and position information from at least threetransmitting platforms by way of a reception antenna onboard the mobileplatform; and computing a local position and a time offset of the mobileplatform using the timing and position information received from the atleast three transmitting platforms, wherein the timing and positioninformation is extracted from packets of data carried byfrequency-modulated continuous-wave signals received from the at leastthree transmitting platforms, the data in each packet including payloadsections made up of multiple symbols and timing header/positionprediction slots made up of multiple supersymbols, wherein the payloadsections and timing header/position prediction slots alternate insequence within the packet, and each timing header/position predictionslot includes a respective timing header and a respective positionprediction section which is contiguous with the respective timingheader. This method may further comprise: computing a time offset of themobile platform using the timing and position information received fromthe at least three transmitting platforms; and adjusting a local clockonboard the mobile platform using the time offset.

A further aspect of the subject matter disclosed in some detail below isa system for determining a position of a mobile platform, comprising amobile platform and at least three transmitting platforms, wherein eachof the at least three transmitting platforms comprises a commonradar/communications transmitter having a transmission antennaconfigured to transmit combined radar/communications waveform-modulatedsignals representing packets of data, the data in each packet includingpayload sections made up of multiple symbols and timing header/positionprediction slots made up of multiple supersymbols, wherein the payloadsections and timing header/position prediction slots alternate insequence within the packet, and each timing header/position predictionslot includes a respective timing header and a respective positionprediction section which is contiguous with the respective timingheader, and wherein the mobile platform comprises a combined radar andcommunications receiver having a common reception antenna, wherein thecommon radar/communications receiver is configured to: receive timingand position information from the at least three transmitting platformsby way of a reception antenna onboard the mobile platform and compute alocal position of the mobile platform using the timing and positioninformation received from the at least three transmitting platforms,wherein the timing and position information is extracted from packets ofdata carried by the frequency-modulated continuous-wave signals receivedfrom the at least three transmitting platforms. Each symbol consists ofan up chirp and a down chirp, and each supersymbol consists of aconcatenation of pairs of up chirps and down chirps of equal chirplengths, the up chirps of the concatenation having the same up phase andthe down chirps of the concatenation having the same down phase. Thesupersymbols in timing headers of the timing header/position predictionslots are phase encoded with time information indicating a duration oftime for which a prediction of the position of the transmitting platformthat transmitted the timing header/position prediction slot was valid;and the supersymbols in position prediction sections of the timingheader/position prediction slots are phase encoded with positioninformation indicating the prediction of the position of thetransmitting platform that transmitted the timing header/positionprediction slot.

Other aspects of systems and methods for enabling time transfer andposition determination in a combined radar/communications system aredisclosed below.

In addition, this disclosure addresses aspects of the algorithm designof a distributive collaborative radar system. More specifically, thesubject matter disclosed in detail below is directed to a system and amethod that enable two or more dispersed platforms to simultaneously userespective FMCW radar systems in a typical radar application such assynthetic-aperture radar for terrain mapping, moving-target indicatorradar to track targets on the ground and air-to-air tracking of otheraircraft. The systems disclosed herein use the same RF spectrum in theiroperation and also communicate through their respective radar systemswhile simultaneously reducing their interplatform interference throughthe use of time and frequency synchronization.

The distributive collaborative radar system disclosed herein solves theimportant problem of simultaneous FMCW radar operation across multipledispersed platforms with enhanced sensitivity while using the same RFspectrum. Thus the radar systems do not have to occupy different RFbands in order to not interfere with each other. And the radar systemsdo not have to restrict their performance to a subset of theiroperational bandwidth, since they can all use the same full bandwidth.It also allows simultaneous communications across this network of radarplatforms using the same transmitted signal.

Although various embodiments of systems and methods for enabling two ormore dispersed platforms to simultaneously operate their respective FMCWradar systems using the same RF spectrum will be described in somedetail below, one or more of those embodiments may be characterized byone or more of the following aspects.

One aspect of the subject matter disclosed in some detail below is adistributive collaborative radar network comprising first and secondradar systems having synchronized respective clocks, wherein each of thefirst and second radar systems comprises a respective commonradar/communications transmitter comprising a transmission antenna and acombined radar and communications receiver comprising a common receptionantenna, a radar receiver connected to the common reception antenna anda communications receiver connected to the common reception antenna. Thecommon radar/communications transmitters of the first and second radarsystems are each configured to convert respective periodic time andposition information into respective timing headers representingsuccessive times and respective position prediction sectionsrepresenting successive positions which are valid for those respectivetimes in a respective packet of data and then transmitfrequency-modulated continuous-wave signals representing the respectivepacket of data. The communications receivers of the first and secondradar systems are each configured to extract timing and positioninformation from received frequency-modulated continuous-wave signalsand compute a respective local position and respective time offset usingthe timing and position information. The common radar/communicationstransmitter of the first radar system is further configured to transmitfrequency-modulated continuous-wave signals having a first chirp slopeand the common radar/communications transmitter of the second radarsystem is further configured to transmit frequency-modulatedcontinuous-wave signals having a second chirp slope. The radar receiverof the first radar system is further configured to demodulate receivedfrequency-modulated continuous-wave signals to form return signals andthen filter out return signals having the second chirp slope when thesecond chirp slope is different than the first chirp slope. The radarreceiver of the second radar system is further configured to demodulatereceived frequency-modulated continuous-wave signals to form returnsignals and then filter out return signals having the first chirp slopewhen the second chirp slope is different than the first chirp slope. Inaccordance with some embodiments, the radar receiver of the first radarsystem is further configured to filter out return signals derived fromfrequency-modulated continuous-wave signals received from beyond amaximum return distance; and the common radar/communications transmitterof the second radar system is further configured to transmitfrequency-modulated continuous-wave signals having the second chirpslope with a start time delay equal to at least a time for thefrequency-modulated continuous-wave signals having the second chirpslope to travel the maximum return distance of the radar receiver of thefirst radar system.

Another aspect of the subject matter disclosed in some detail below is adistributive collaborative radar network comprising first and secondradar systems having synchronized respective clocks, wherein each of thefirst and second radar systems comprises a respective commonradar/communications transmitter comprising a transmission antenna and acombined radar and communications receiver comprising a common receptionantenna, a radar receiver connected to the common reception antenna anda communications receiver connected to the common reception antenna. Thecommon radar/communications transmitters of the first and second radarsystems are each configured to convert respective periodic time andposition information into respective timing headers representingsuccessive times and respective position prediction sectionsrepresenting successive positions which are valid for those respectivetimes in a respective packet of data and then transmitfrequency-modulated continuous-wave signals representing the respectivepacket of data. The communications receiver of the first and secondradar systems are each configured to extract timing and positioninformation from received frequency-modulated continuous-wave signalsand compute a respective local position and respective time offset usingthe timing and position information. The common radar/communicationstransmitter of the first radar system is further configured to transmitfrequency-modulated continuous-wave signals having a first chirp slope.The radar receiver of the first radar system is further configured tofilter out return signals derived from frequency-modulatedcontinuous-wave signals received from beyond a maximum return distance.The common radar/communications transmitter of the second radar systemis further configured to transmit frequency-modulated continuous-wavesignals having a second chirp slope with a start time delay equal to atleast a time for the frequency-modulated continuous-wave signals havingthe second chirp slope to travel the maximum return distance of theradar receiver of the first radar system. In accordance with someembodiments, the radar receiver of the first radar system is furtherconfigured to filter out return signals having the second chirp slopeand the radar receiver of the second radar system is further configuredto filter out return signals having the first chirp slope when thesecond chirp slope is different than the first chirp slope.

Yet another aspect is a method for reducing interference between radarsystems of a distributive collaborative radar network, comprising:synchronizing first and second radar systems of a distributivecollaborative radar network in time and frequency of transmission;transmitting frequency-modulated continuous-wave signals comprisingsymbols and supersymbols comprising respective position information fromthe first and second radar systems, wherein the first radar systemtransmits frequency-modulated continuous-wave signals having a firstchirp slope and the second radar system transmits frequency-modulatedcontinuous-wave signals having a second chirp slope; receiving at thefirst radar system frequency-modulated continuous-wave signals; mixingfrequency-modulated continuous-wave signals received by the first radarsystem with frequency-modulated continuous-wave signals transmitted bythe first radar system and outputting return signals; using a firstdemod/remod filter in the first radar system to filter out returnsignals having the second chirp slope when the second chirp slope isdifferent than the first chirp slope and not filter out return signalshaving the second chirp slope when the second chirp slope is the same asthe first chirp slope; and estimating a range and a velocity of a targetobject relative to the first radar system based on beat frequenciesderived from the return signals not filtered out by the firstdemod/remod filter.

In accordance with some embodiments of the method described in theimmediately preceding paragraph, the method further comprises: receivingat the second radar system frequency-modulated continuous-wave signals;mixing frequency-modulated continuous-wave signals received by thesecond radar system with frequency-modulated continuous-wave signalstransmitted by the second radar system and outputting return signals;using a second demod/remod filter in the second radar system to filterout return signals having the first chirp slope when the second chirpslope is different than the first chirp slope and not filter out returnsignals having the first chirp slope when the second chirp slope is thesame as the first chirp slope; and estimating a range and a velocity ofa target object relative to the second radar system based on beatfrequencies derived from the return signals not filtered out by thesecond demod/remod filter. In accordance with other embodiments, themethod further comprises using high and low pass filters in the firstradar system to filter out return signals derived fromfrequency-modulated continuous-wave signals received from beyond amaximum return distance, wherein the frequency-modulated continuous-wavesignals transmitted by the second radar system have a start time delayequal to at least a time for the frequency-modulated continuous-wavesignals having the second chirp slope to travel the maximum returndistance of the radar receiver of the first radar system.

Other aspects of systems and methods for enabling two or more dispersedplatforms to simultaneously operate their respective FMCW radar systemsusing the same RF spectrum are disclosed below.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, functions and advantages discussed in the precedingsection may be achieved independently in various embodiments or may becombined in yet other embodiments. Various embodiments will behereinafter described with reference to drawings for the purpose ofillustrating the above-described and other aspects.

FIG. 1 is a graph representing received and transmitted frequencies of atriangular chirp waveform in which the up and down ramps have equal timedurations. The solid lines represent the transmitted signal; the dashedlines represent the reflected and received signal.

FIG. 2A is a graph showing a symbol design using linear frequencymodulation to include one up chirp and one down chirp in each symbol.

FIG. 2B is a graph representing frequencies of chirp waveforms beingtransmitted in separate parallel channels.

FIG. 3 is a block diagram identifying some components of a FMCW radarsystem that is not configured to use the combined radar/communicationswaveform disclosed herein.

FIG. 4 is a block diagram identifying some components of a combinedradar/communications system configured in accordance with one embodimentto use the combined radar/communications waveform disclosed herein.

FIG. 5 is a block diagram that simplifies FIG. 4 by reducing thecomponents of the combined radar/communications system to a singleblock.

FIG. 6A is a diagram representing the format of a standard packet.

FIG. 6B is a diagram representing the format of an enhanced packetcontaining supersymbols.

FIG. 7 is a graph of standard deviation of parameter error versus SNR(dB) that shows the performance of a linear chirp parameter estimationmethod for a sub-sample length of N=1000. The solid, dashed and dottedlines respectively represent the errors in parameters a, b and c, whichrespectively control the chirp slope (a.k.a. chirp rate), initialfrequency and initial phase of the chirp signal.

FIG. 8 is a graph of the probability of symbol error versus relative SNR(dB) as a function of supersymbol length derived by computer simulation.

FIG. 9 is a block diagram identifying some components of a system fortiming and position processing in accordance with one embodiment whichhas been added to (and may be incorporated in) a combinedradar/communications system that transmits and receives using fixedantennas.

FIG. 10 is a block diagram identifying some components of a system fortiming and position processing in accordance with another embodimentwhich has been added to (and may be incorporated in) a combinedradar/communications system that transmits and receives using steerableantennas.

FIG. 11 is a block diagram identifying the same components identified inFIG. 10, but with the addition of an intentional beam jitter subsystemin accordance with a further embodiment.

FIG. 12 is a polar plot of a normalized antenna radiation pattern for auniform linear array having four elements with 0-degree boresightpointing angle with a ground plane that eliminates any backsideradiation.

FIG. 13 is a graph showing how the plots (plotted in rectangularcoordinates) of normalized antenna radiation patterns (directivityversus direction angle) vary with array size for simulated uniformlinear arrays with 4, 16, 64 and 256 elements respectively.

FIG. 14 is a graph showing the angular distribution of SNR relative tothe mainbeam for a simulated uniform linear array having 64 elements.

FIG. 15 is a block diagram showing the operation of an intentional beamjitter system that is part of a combined radar/communications system.

FIGS. 16A through 16D are graphs showing the effects of intentional beamjitter on both sidelobe and mainlobe performance for simulated uniformlinear arrays with 4, 16, 64 and 256 elements respectively for afrequency of 800 MHz.

FIG. 17A is a diagram showing a first FMCW platform receiving time andposition information from three other FMCW platforms in the course ofconcurrent combined radar and communications operations.

FIG. 17B is a diagram showing two FMCW platforms with their interferingradar “returns”.

FIG. 18 is a graph showing start times and delay ranges for adistributed FMCW system.

FIG. 19 is a flowchart showing the operation of a FMCW radar network inaccordance with one embodiment.

FIG. 20 is a flowchart identifying operations performed by a demod/remodfilter in accordance with one embodiment.

FIG. 21 is a block diagram identifying components of a subsystem forcomputing the unwrapped phase of a real signal.

FIGS. 22-24 are diagrams symbolically representing electronic circuitryfor respectively digitally computing the values of three terms in anequation for estimating a slope coefficient representing a chirp slopein accordance with one embodiment.

FIG. 25 is a flowchart identifying processing steps for basebandcommunications processing in accordance with one embodiment.

Reference will hereinafter be made to the drawings in which similarelements in different drawings bear the same reference numerals.

DETAILED DESCRIPTION

Illustrative embodiments of systems and methods for enabling timetransfer and position determination in a combined radar/communicationssystem and for enabling two or more dispersed platforms tosimultaneously operate their respective FMCW radar systems using thesame RF spectrum are described in some detail below. However, not allfeatures of an actual implementation are described in thisspecification. A person skilled in the art will appreciate that in thedevelopment of any such actual embodiment, numerousimplementation-specific decisions must be made to achieve thedeveloper's specific goals, such as compliance with system-related andbusiness-related constraints, which will vary from one implementation toanother. Moreover, it will be appreciated that such a development effortmight be complex and time-consuming, but would nevertheless be a routineundertaking for those of ordinary skill in the art having the benefit ofthis disclosure.

Radar signals typically fall into two categories: pulsed signals andcontinuous signals. Pulsed signals are on for a short period of time andthen turn off and wait for a returned echo. In contrast, FMCW radartypically uses a frequency-modulated continuous signal that bounces offthe targets continuously and returns to the receiver. In particular, alinear frequency sweep is usually applied and the returned signal can bemixed with the transmitted signal to produce a single expected tone foreach target return. This linear frequency sweep is also called a linearchirp or linear frequency-modulated signal. There are a number ofadvantages to using FMCW radar in comparison to pulsed radar.

The innovative technology disclosed herein enables time transfer andposition determination services during operation of a combinedradar/communications system. For example, the combinedradar/communications system disclosed in U.S. patent application Ser.No. 15/988,112 uses a common set of programmable hardware and softwareto implement both radar and communications functions in a flexiblemanner so that one system can provide both of the required radar andcommunications performances.

The communications function disclosed herein uses digital modulation, inwhich changes in phase, magnitude and frequency are used to representdigital information. In a digital modulation scheme, each transmittedbit (or groups of bits) is mapped to a particular state of the carrierwave. As used herein, the term “symbol” means the state of the carrier,which is defined as having a specific phase, magnitude and frequency.The rate at which the carrier changes state from one symbol to the nextis called the symbol rate.

Radar and communications system requirements force design choices withrespect to the amount of signal power. The respective optimum signalstrengths are described briefly below, emphasizing the differences. Fora combined system, both signal strength criteria should be met.

A radar's principle of operation is based on the properties ofelectromagnetic waves and their characteristic reflection by differentmaterials. First, a radio signal of frequency f and wavelength λ=c/f istransmitted. Based on the reflected and received signal response,measurements regarding direction, distance, and relative velocity of thereflecting target can be made. The received signal strength of thetarget can be calculated from the radar equation:

$P_{r} = {{\frac{P_{t}G_{t}A_{r}\sigma_{S}}{( {4\pi} )^{2}R^{4}}\mspace{14mu}{with}\mspace{20mu} A_{r}} = \frac{G_{r}\lambda^{2}}{4\pi}}$In the above expression, P_(r) denotes the received signal strength,while P_(t) represents the transmitted signal power. The antenna ischaracterized by its transmit and receive antenna gains G_(t) and G_(r)respectively as well as the corresponding effective aperture A_(r) ofthe receiving antenna. σ_(S) is the scattering cross section of thereflecting target which is located at the distance R. The receivedsignal strength degrades with the fourth power of range. This is incontrast to general communication systems which only degrade with thesecond power of range. Thus, for the communications case, the powerP_(c) received by the communications receiver (at a range R from thetransmitter, instead of co-located) has no reflection and only an R²loss, and may be expressed as

$P_{c} = {{\frac{P_{t}G_{t}A_{r}A_{c}}{4\pi^{2}R^{4}}\mspace{14mu}{with}\mspace{20mu} A_{c}} = \frac{G_{c}\lambda^{2}}{4\pi}}$where A_(c) is the aperture of the receiving communications antenna withits associated gain G_(c). Therefore, the radar receiver has to providea higher sensitivity and dynamic range in order to cover a wide range oftarget distances. What this means is that with a commonradar/communications signal and hence a common antenna and transmitpower, the maximum return range (also referred to herein as “maximumreturn distance”) of the radar signal R_(max) is typically much lessthan the range of the communications signal R_(comm), i.e.,R_(max)<R_(comm).

The transmitted linear frequency-modulated signal of an FMCW radarsystem can be modeled as a linear chirp:s _(T)(t)=cos(2πf _(c) t+2π∫₀ ^(T) f _(T)(τ)dτ)where f_(T)(τ)=(B/T)τ is the transmit frequency as a linear function oftime τ (for an up ramp; a down ramp would be negative), f_(c) is thecarrier frequency, B is the bandwidth, the amplitude is normalized tounity, and T is the time duration. Considering a reflected and receivedsignal with a time delay t_(d)=2(R₀+vt)/v_(c) and a Doppler shiftf_(D)=−2·f_(c)v/v_(c), where v_(c) is the velocity of light (for RFsignals), the received frequency after mixing the transmitted signalwith the received signal can be expressed as

${f_{R}(t)} = {{\frac{B}{T}( {\tau - t_{d}} )} + f_{D}}$where R₀ is the range at time t=0 and v is the target velocity (or rangerate). Thus the received up ramp signal can be described as

${s_{R}(t)} = {\cos( {2{\pi( {{f_{c}( {\iota - t_{d}} )} + {\frac{B}{T}( {\frac{t^{2}}{2} - {t_{d}t}} )} + {f_{D}t}} )}} )}$Here the received signal amplitude is normalized to unity. In fact, thereceived signal amplitude depends on antenna gains, transmitted power,the target's distance and radar cross section (RCS). To obtaininformation about the Doppler frequency and beat frequency, thetransmitted signal s_(T)(t) and the received signal s_(R)(t) are mixedby multiplication in the time domain and passed to a low-pass filter(LPF) with a bandwidth B. The intermediate frequency (IF) signals_(IF)(t) of the LPF output is then obtained for an up ramp as

${s_{IF}(t)} = {\frac{1}{2}{\cos( {{2{\pi( {f_{c} \cdot \frac{2R_{0}}{v_{c}}} )}} + {2{\pi( {{\frac{2R_{0}}{v_{c}} \cdot \frac{B}{T}} + \frac{2f_{c}v}{v_{c}}} )}t}} )}}$Similarly, the IF signal s_(IF)(t) of the LPF output can be obtained forthe down ramp (with the same slope as the up ramp, but the oppositesign) as follows

${s_{IF}(t)} = {\frac{1}{2}{\cos( {{2{\pi( {f_{c} \cdot \frac{2R_{0}}{v_{c}}} )}} + {2{\pi( {{{- \frac{2R_{0}}{v_{c}}} \cdot \frac{B}{T}} + \frac{2f_{c}v}{v_{c}}} )}t}} )}}$Hence, two time-dependent frequency terms called the up and down rampbeat frequencies appear in the spectrum of the baseband signal:

$\begin{matrix}{f_{bu} = {{\frac{2R_{0}}{\nu_{c}} \cdot \frac{B}{T}} + \frac{2f_{c}v}{\nu_{c}}}} & (1) \\{f_{bd} = {{{- \frac{2R_{0}}{v_{c}}} \cdot \frac{B}{T}} + \frac{2f_{c}\nu}{v_{c}}}} & (2)\end{matrix}$These frequencies may be used to solve for target velocity v and rangeR₀. (The references: Rohling and Meinecke, “Waveform design principlesfor automotive radar systems”, 2001 CIE International Conference onRadar (2001), and Rohling and Moller, “Radar waveform for automotiveradar systems and applications”, 2008 IEEE Radar Conference, 26-30 May(2008), contain this information and references to the papers where thefrequencies are derived.) FIG. 1 shows the frequencies for thetransmitted (solid lines) and received (dashed lines) signals having atriangular waveform, where f_(bu) and f_(bd) denote the up ramp beatfrequency and down ramp beat frequency, respectively.

This disclosure proposes to use a combined waveform having a design thatis based on the above-described up and down chirps, so that the radarfunction is essentially unaffected, but is parameterized in two ways toallow communications to take place:

(1) Each symbol will be of length 2T and have two chirps, one up and onedown. Note that one could also use a down chirp followed by an up chirp.The following discussion standardizes on up, then down chirps. The upchirp will start with a frequency f_(c)−B/2 at time 0 and then go to afrequency f_(c)+B/2 at time T_(i); then the complementary down chirpwill start with a frequency f_(c)+B/2 at time T_(i) and end at afrequency f_(c)−B/2 at time 2T for symbol i. Let the two different chirpslopes be labeled a_(i) and a_(i), and the two different frequencies belabeled b_(i) and β_(i). Their values can be related to the chirpparameters by a_(i)=B/T_(i), b_(i)=f_(c)−B/2, a_(i)=−B/(2T−T_(i)), andβ_(i)=f_(c)+B/2.

(2) Each symbol will have a separate initial phase for each chirp: phasec_(i) for the first chirp and phase γ_(i) for the second chirp. Here−π<c_(i), γ_(i)≤π or in normalized form: −½<c_(i), γ_(i)≤½ in thefollowing equations.

These changes will not impact the radar performance of the waveform atall. The only changes to derive range and range rate have to do withmeasuring the beat frequency during the two intervals [0, T_(i)] and[T_(i), 2T], instead of the two intervals [0, T] and [T, 2T]. Theequations for the two intervals can be represented in the followingforms:exp(2πj(a _(i) t ² +b _(i) t+c _(i))), 0≤t<T _(i)exp(2πj(α_(i)(t−T _(i))²+β_(i)(t−T _(i))+γ_(i))), T _(i) ≤t<2T

In its most general form, the CRCW can be represented by multipleparallel (contiguous or non-contiguous) channels (m in number) havingfrequency bands B_(i), where i=1, 2, . . . , m. Each frequency band hasits own symbol times, chirp slopes and phases within an overall range offrequencies having a total bandwidth B_(T) that represent all the radarand communications systems that are currently operating. FIG. 2B showsthis design in which a respective series of symbols, each symbolincluding an up chirp and a down chirp as described above, aretransmitted in respective channels of width B centered on respectivedifferent carrier frequencies.

Henceforth, this disclosure concentrates on the canonical case with onechannel with contiguous bandwidth B and center frequency f_(c).

In accordance with the methodology disclosed herein, symbols havingwaveforms of the types depicted in FIG. 2A may be transmittedconcurrently. Similarly, the reflected and returned signals may beprocessed in parallel to derive various parameters characterizing thetargets detected by the FMCW radar system.

The range resolution ΔR represents the minimum discernible range of twotargets with the same velocity, and the velocity resolution Δvrepresents the minimum discernible velocity of two targets with the samerange. The required bandwidth B is related to the given range resolutionΔR and can be formulated as

$B \geq \frac{v_{c}}{2\Delta R}$Similarly, the observation time T is related to the velocity resolutionΔv and can be expressed as

$T \geq \frac{\nu_{c}}{2f_{c}\Delta v}$The Nyquist sampling theorem then requires

${f_{s}({radar})} \geq {\frac{2{BR}_{\max}}{v_{c}T} + \frac{2f_{c}v_{\max}}{\nu_{c}}}$in order to not have the maximum beat frequency fold over in thefrequency domain. In order that the maximum return does not fold over inthe time domain (folding into the next time interval T), a similarrequirement is that

$t_{d} = {{2\frac{R_{\max} + {\nu_{\max}T}}{v_{c}}} < T}$ or$T > \frac{2R_{\max}}{\nu_{c}}$for reasonable velocities. These equations give a relationship betweenthe radar performance parameters {R_(max), v_(max), ΔR, Δv,f_(c)} andthe waveform parameters {B, T, f_(s)}. Note that for a given CRCW symbolwith durations T_(i) and 2T−T_(i) for the two chirps, T in the aboveequations would be replaced by one of these two quantities depending onwhich part of the symbol is being referred to.

For communications functions using the CRCW, one may take the desiredmaximum data rate for communications in each channel m and find abandwidth B_(m) that will support that through standard communicationsanalysis. The result is an available total bandwidth B_(T). Then clearly

${\sum\limits_{m}B_{m}} \leq B_{T}$The sample rate of the communications receiver f_(s)(comm) after downconversion must satisfy the condition:f _(s)(comm)≥2B _(m)for each channel in order to capture the full bandwidth of thecommunicated signal.

For simplicity, the following additional disclosure assumes that eachchannel bandwidth is the same value B, meaning that the subscript inwill be dropped. Suppose there are S symbols from a set {S_(k)} definedby {T, T_(i), B, Θ_(j), Φ_(l)} (where 0<T_(i)<2T, 0≤i≤C−1, and −π<Θ_(j),Φ_(l)<π, j≥0, l≤C_(l)−1, C·C₁ ²=S), where T_(i) is the length of time ofthe first chirp, B is the corresponding frequency range for both chirps(all symbols will have the same bandwidth and it is the same for both upand down chirps), and Θ_(j) and Φ_(l) are the corresponding phases ofthe up and down ramps.

To support a required data rate A bits per second, one should haveΛ≤└ log₂(S)┘/2T└B _(T) /B┘where └ log₂(S)┘ is the number of bits/symbol, ½T is the number ofsymbols per second, and B_(T) is the total bandwidth allocated (viaregulation, hardware limits, etc.) for the combined radar/communicationssystem. If all of the limits on the chirp periods are combined, theresult is

$T_{i},{{{2T} - T_{i}} \geq T_{\min} \geq {\max\{ {\frac{2R_{\max}}{v_{c}},\ \frac{v_{c}}{2f_{c}\Delta v}} \}}}$and T ≥ T_(max) ≥ max {T_(i), 2T − T_(i)}.Similarly,

log₂S ≥ 2Λ T/⌊B_(T)/B⌋ and$f_{s} \geq {\max\{ {B,{\frac{2BR_{\max}}{v_{c}T} + \frac{2f_{c}\nu_{\max}}{v_{c}}}} \}}$

Let the number of unique chirp times (the unique values in {T_(i)}) (orequivalently the number of unique positive frequency slopes for thesymbol set) be C. These conditions can be met via the followingequations:T=(T _(min) +T _(max))/2T _(i) =T _(min)+(T _(max) −T _(min))·i/(C−1)for i=1, . . . , C−1 as an example. Then the complementary duration2T−T _(i) =T _(max)−(T _(max) −T _(min))·i/(C−1)is simply the reverse list of the {T_(i)}, simplifying the receiver andtransmitter design.

With no other limits on the phases and a symbol defined by a phase pair(Θ, ϕ)there can be D=┌√{square root over (S/C)}┐ unique values of each phasefor both coordinates for a total of D² phases for each slope C. Thus thetotal number of symbols would then beC·D ² =C·┌√{square root over (S/C)}┐·┌√{square root over (S/C)}┐which is greater than S as required. A simple assumption is to spreadthe phases evenly over (−π, π] via the following phase definitions:Θ_(j)=−π+2πj/C _(l)Φ_(l)=−π+2πl/C _(l)for j, l=1, . . . , D−1.

Together (both radar and communication cases), the above description hasdefined almost all of the basic waveform parameters{S,B,T,f _(s) ,{T _(i)},{Φ_(j)},{Θ_(l)}}using the requirement/design parameters{R _(max) ,v _(max) ,ΔR,Δv,f _(c) ,B _(T),Λ}.

Note that the amplitude A (which was normalized to unity in the abovediscussion) has not been discussed because amplitude is better handledthrough the link budget and RF front-end hardware, which are purelyapplication specific, as described above. The remaining values C and Dgive a way to adjust the spread of symbols so as to give the best andmost consistent symbol detection performance as a function of SNR. Thisbalance of slope versus phase (C and D) is described in the followingparagraphs.

A method for balancing symbol slopes and phases will now be described insome detail. The following discrete chirp model will be used in order toestimate variance:s[n]=A exp(j(2πj(αm ² +βn+γ))z[n]=s[n]+w[n]m=n−(N−1)/2, 0≤n≤N−1  (3)where s[n] is the sampled version of a symbol, z[n] is the sampledreceived signal plus noise, and w[n] is the sampled version of thereceived noise with a standard deviation of 3σ. The value N is thenumber of samples during the chirp period. The parameters {α, β, γ}define each chirp of the two-chirp set that corresponds to a symbol andrespectively correspond to chirp rate (or frequency slope of chirp),frequency and phase. This disclosure employs modified approximations tothe Cramer-Rao lower bound for the variance estimators of each parameterusing the following notation:

$\begin{matrix}{{{var}\{ \overset{\hat{}}{\alpha} \}} \gtrsim {( \frac{\sigma}{\pi\; A} )^{2}\frac{90}{NT^{4}}}} & (4) \\{{{var}\{ \overset{\hat{}}{\beta} \}} \gtrsim {( \frac{\sigma}{\pi A} )^{2}\frac{6}{NT^{2}}}} & (5) \\{{{var}\{ \overset{\hat{}}{\gamma} \}} \gtrsim {( \frac{\sigma}{\pi A} )^{2}\frac{9}{8N}}} & (6)\end{matrix}$This information can be used to choose a balance between the number C ofdifferent frequency slopes and number D of different phases.

A specific example will now be described to show how to balance thevalues of C and D as a function of the other waveform parameters.Suppose that B=1 MHz and T_(min)=10 μs. And suppose that the chirpbandwidths for the symbols are equally spaced in frequency. Inparticular, assume that the maximum slope is

$\alpha_{\max} = \frac{B}{T_{\min}}$and then distribute the frequency slope values evenly to cover the fullrange to this maximum. This equation follows from the followingobservations. The Doppler equation relates transmit frequency f versusapparent observed frequency f′ due to relative motion. So

$f^{\prime} = {\frac{v_{c} + v_{0}}{v_{c} + v_{s}}f}$where v_(c) is the velocity of the signal (the velocity of light for RFsignals), v₀ is the signed velocity of the observer, and v_(s) is thesigned velocity of the source (transmitter). Thus the received chirp maybe shifted in frequency from the transmitted chirp by the ratio(v_(c)+v₀)/(v_(c)+v_(s)). This essentially changes the value of β of thereceived signal to

$\beta^{\prime} = {\frac{v_{c} + v_{0}}{v_{c} + v_{s}}\beta}$where β is the starting frequency of the transmitted chirp and β′ is thestarting frequency of the received chirp. Because of the way thereceived signal is processed (described in some detail below), theestimation of β may be avoided without affecting receiver performance.

Some components of a simplified FMCW radar system 100 that is notconfigured to use the waveforms disclosed hereinabove are identified inFIG. 3. The FMCW radar system 100 may installed on a vehicle such as acar, a bus, a truck, etc., for measuring the range of a radar target102, such as another vehicle or a person, and sending out an alarmsignal when the measured range is less than a specified minimumseparation distance. The FMCW radar system 100 is functionally dividedinto a transmission portion and a reception portion. The transmissionportion includes an up/down ramp controller 104, a digital-to-analog(D/A) converter 105, a frequency-modulated continuous waveform generator106, a voltage-controlled oscillator (VCO) 107, a transmission amplifier108, and a transmission antenna 110 connected in series. The receptionportion includes a reception antenna 116, a low-noise receptionamplifier 118, a frequency mixer 120 (which is also connected to VCO107), a low-pass filter 122, an analog-to-digital (A/D) converter 124,and a baseband radar signal processing module 126 (which is alsoconnected to the up/down ramp controller 104) connected in series. Amodulated signal is transmitted and received through the antennas, andthe transmitted and received signals are multiplied in the time domain,filtered and processed to find the peaks in frequency which correspondto target returns. The final result is a stream of measurementsincluding range and range rate (relative velocity) of all the targetspresent.

Sensing operations of the FMCW radar system 100 can be briefly describedas follows. The up/down ramp controller 104 outputs digital controlsignals to the digital-to-analog converter 105, which converts thedigital signals into analog signals that control the frequency-modulatedcontinuous waveform generator 106 to generate frequency-modulatedcontinuous waveforms, which the VCO 107 converts to FMCW signals havinga carrier frequency f_(c)(Tx). The FMCW signals are amplified bytransmission amplifier 108 and emitted as RF electromagnetic waves 112toward the radar target 102 by the transmission antenna 110.Correspondingly, the reception antenna 116 receives RF electromagneticwaves 114 reflected from the radar target 102. The reception antenna 116acts as a transducer to convert the reflected RF electromagnetic wavesinto electrical signals which are amplified by low-noise receptionamplifier 118. The frequency mixer 120 then frequency mixes the receivedsignals output by the low-noise reception amplifier 118 with thetransmitted signals having a carrier frequency f_(c)(Tx) generated bythe VCO 107 to produce first demodulated signals that contain phaseinformation. The low-pass filter 122 performs low-pass filtering toobtain beat frequency signals between the transmitted and receivedsignals. The analog-to-digital converter 124 samples the beat frequencysignals and converts the beat frequency signals into digital signals. Inorder to compute information of the targets such as ranges and rangerates, the baseband radar signal processing module 126 is configured toconvert the digital beat frequency signals from the time domain to thefrequency domain. A common method is using fast Fourier transforms. Theup and down chirp signals are processed separately in two fast Fouriertransforms. After fast Fourier transformation, the baseband radar signalprocessing module 126 finds the peaks in frequency, which correspond totarget returns, utilizing a threshold value. The beat frequencies arethen used to solve for target velocity v and range R₀, as previouslydescribed. The final result is a stream of measurements of range andtarget velocity (or range rate) for all targets present. In the exampledepicted in FIG. 3, the baseband radar signal processing module 126 isconfigured to compute and derive information about the target 102, suchas range and range rate, and then store these radar measurements 128 ina non-transitory tangible computer-readable storage medium.

By contrast, with a modification to the FMCW radar system partlydepicted FIG. 3, a combined radar/communications system may beconfigured to use the previously described CRCW. FIG. 4 is a blockdiagram identifying some components of a combined radar/communicationssystem 130 configured to use the CRCW disclosed herein. In the examplepartly depicted in FIG. 4, data may be transmitted from the combinedradar/communications system 130 (which is part of a communicationsplatform #1) to a communications platform 132 (also referred to hereinas “communications platform #2”). Conversely, data may be transmittedfrom the communications platform 132 to the combinedradar/communications system 130 of communications platform #1. Thus thecombined radar/communications system 130 has both radar andcommunications data output and radar and communications data input. Theradar portion is essentially unchanged from what is depicted in FIG. 3,merely requiring non-uniform symbol timing beyond the simpler FMCW radarsystem, which only needed uniform timing of the up or down chirp tocompute the range and range rate. The processing of the waveform by thecommunications receiver (the uppermost processing path in FIG. 4) willbe described in more detail later with reference to FIGS. 19-23.

As depicted in FIG. 4, the combined radar/communications system 130includes a local transmitter and a local receiver which combine bothradar and communications signals. The remote communications platform 132(communications platform #2) that is communicating with combinedradar/communications system 130 of communications platform #1 wouldtypically use a different frequency band or bands for itscommunications. Thus FIG. 4 shows two different frequencies: fc_Tx(equal to f_(c)(Tx)) for the center frequency of the transmitter of thecombined radar/communications system 130 (and of the radar receiver) andfc_Rx (equal to f_(c)(Rx)) for the center frequency of thecommunications receiver of the combined radar/communications system 130,which from the point of view of the remote communications platform 132is the center frequency for its transmitter.

To clarify the terminology used herein, modulation is a process by whicha carrier signal is altered according to information in a messagesignal. The transmission frequency f_(c)(Tx) is the frequency of thecarrier signal transmitted by a transmitter. The signal received by areceiver is demodulated using the same frequency. The demodulated signalis then sampled by the receiver. The sampling rate is the rate at whichthe message signal is sampled. The frequency of the carrier signal isusually much greater than the highest frequency of the input messagesignal. The Nyquist sampling theorem requires that the sampling ratef_(s) be greater than two times the sum of the carrier frequency and thehighest frequency of the modulated signal in order for the demodulatorto recover the message correctly. To modulate a signal using digitalmodulation with an alphabet having M symbols, one may start with a realmessage signal whose values are integers from 0 to M−1.

In the example depicted in FIG. 4, the transmission antenna 110 of thecombined radar/communications system 130 is transmitting RFelectromagnetic waves having a transmit center frequency f_(c)(Tx)toward a radar target 102 and toward a communications platform 132. Inreturn, the reception antenna 116 of the combined radar/communicationssystem 130 receives RF electromagnetic waves from the radar target 102having a frequency equal to the center frequency f_(c)(Tx) plus theDoppler frequency due to movement of the radar target 102 relative tothe combined radar/communications system 130. The reception antenna 116also receives RF electromagnetic waves from the communications platform132 having a frequency equal to the center frequency f_(c)(Rx)transmitted by the transmission antenna (not shown in FIG. 4) of thecommunications platform 132 plus the Doppler frequency due to movementof the communications platform 132 (communications platform #2) relativeto the communications platform #1. As previously mentioned, the separatereceive frequency channel for communications from the communicationsplatform 132 uses a different center frequency f_(c)(Rx) than thetransmit center frequency f_(c)(Tx) so that the two radar/communicationstransmitters do not transmit in the same frequency band.

Referring to FIG. 4, the transmitting portion (hereinafter “commonradar/communications transmitter 131”) of the combinedradar/communications system 130 of communications platform #1 includesthe following components connected in series: a communications datasource 134 that stores data to be transmitted to communications platform132; a digital modulation symbol generator 136 that converts thecommunications data to symbols; a digital-to-analog converter 105 thatconverts the digital symbols to analog symbols; a combinedradar/communications waveform generator 106′ that converts the analogsymbols received from the digital-to-analog converter 125 intooscillator control voltages; a VCO 107 that applies a modulating signalto a carrier signal having a transmit frequency f_(c)(Tx) based on thevoltage control inputs and outputs CRCW-modulated signals; atransmission amplifier 108 that amplifies the resulting CRCW-modulatedsignals received from VCO 107; and a transmission antenna 110 thatbroadcasts the CRCW-modulated signals received from transmissionamplifier 108.

Still referring to FIG. 4, the radar receiver and communicationsreceiver (hereinafter collectively referred to as the “combinedradar/communications receiver 133”) of the combined radar/communicationssystem 130 both receive signals via a reception antenna 116 and alow-noise reception amplifier 118. In the next paragraph, additionalcomponents of the radar receiver of the combined radar/communicationsreceiver 133 will be described. Thereafter, additional components of thecommunications receiver of the combined radar/communications receiver133 will be described.

The radar receiver of the combined radar/communications system 130includes reception antenna 116, low-noise reception amplifier 118, afrequency mixer 120 a (which is also connected to VCO 107), a low-passfilter 122 a with a bandwidth B, an analog-to-digital converter 124 a,and a baseband radar signal processing module 126 (which is alsoconnected to the digital modulation symbol generator 136) connected inseries. The reception antenna 116 receives RF electromagnetic wavesreflected from the radar target 102. The reception antenna 116 convertsthe reflected RF electromagnetic waves into electrical signals which areamplified by low-noise reception amplifier 118. The frequency mixer 120a then frequency mixes the amplified signals output by the low-noisereception amplifier 118 with the signals having a carrier frequencyf_(c)(Tx) generated by the VCO 107 to produce first demodulated signalscontaining phase information. The low-pass filter 122 a performslow-pass filtering to obtain beat frequency signals between thetransmitted and received signals. The analog-to-digital converter 124 asamples the beat frequency signals and converts the beat frequencysignals into digital signals. The baseband radar signal processingmodule 126 is configured to convert the digital beat frequency signalsfrom the time domain to the frequency domain using separate fast Fouriertransforms for the up and down chirp signals. After fast Fouriertransformation, the baseband radar signal processing module 126 findsthe peaks in frequency, which correspond to target returns, utilizing athreshold value. The beat frequencies are then used to solve for targetvelocity v and range R₀, as previously described. The final result is astream of measurements of range and target velocity (or range rate) forall targets present. In the example depicted in FIG. 4, the basebandradar signal processing module 126 is configured to compute and deriveinformation about the radar target 102, such as range and range rate,and then store these radar measurements in a non-transitory tangiblecomputer-readable storage medium 128.

The communications receiver of the combined radar/communications system130 includes the reception antenna 116, the low-noise receptionamplifier 118, a frequency mixer 120 b (which is connected to a VCO 142that applies a modulating signal of frequency f_(c)(Rx) to the voltagecontrol input from waveform generator 144, a low-pass filter 122 b witha bandwidth B, an analog-to-digital converter 124 b, and a basebandcommunications signal processing module 138 connected in series. Thereception antenna 116 receives RF electromagnetic waves transmitted bythe transmitter of the remote communications platform 132. The frequencymixer 120 b frequency mixes the received signals output by the low-noisereception amplifier 118 with the signals having a carrier frequencyf_(c)(Rx) generated by the VCO 142 to produce second modulated signalscontaining phase information. The low-pass filter 122 b performslow-pass filtering. The analog-to-digital converter 124 a samples thefiltered signals and converts those analog signals into digital signals.The baseband communications signal processing module 138 is configuredto decode the digitals signals to extract the received communicationsdata 140, which is then stored in a non-transitory tangiblecomputer-readable storage medium.

As shown in FIG. 4, the baseband radar signal processing is only changedin a minor way to use the up and down chirped signals containing thecommunicated data. Basically, instead of processing up and down chirpswith identical duration, the radar processing would process the receiveddata by mixing with the transmitted non-uniform up and down chirps anddoing the same calculations as in traditional FMCW processing. Fouriertransforms together with Eqs. (1) and (2), which relate the beatfrequency to range and range rate (or relative velocity), can beprocessed in the same manner as in typical FMCW radar. The controllingequations become

$\begin{matrix}{f_{bu} = {{\frac{2R_{0}}{v_{c}} \cdot \frac{B}{T_{i}}} + \frac{2f_{c}v}{\nu_{c}}}} & (7) \\{f_{bd} = {{{- \frac{2R_{0}}{\nu_{c}}} \cdot \frac{B}{{2T} - T_{i}}} + \frac{2f_{c}v}{\nu_{c}}}} & (8)\end{matrix}$when a symbol with slope dictated by T_(i) is sent. From theseequations, range R₀ and range rate v can be effectively estimated.

As described above, the basic FMCW system consists of a transmitter, areceiver and a mixer. A modulated signal is transmitted and received,and the transmitted and received signals are multiplied in the timedomain and processed. More specifically, the process typically involvesat least the following steps: (1) calculate the transmitted signal; (2)calculate the received signal; (3) mix the signals by multiplying in thetime domain; (4) filter out one of the two derived sinusoidal terms; and(5) perform FFT on the filtered signal. FMCW processing is described indetail in many papers and books (see, e.g., Wu and Linnartz, “DetectionPerformance Improvement of FMCW Radar Using Frequency Shift”, Symposiumon Information Theory and Signal Processing in the Benelux, Brussels,Belgium, May 10-11, 2011 and Parrish, “An Overview of FMCW Systems inMATLAB”) and is not further described herein.

FIG. 5 is a block diagram that simplifies FIG. 4 by reducing thecomponents of the combined radar/communications system 130 to a singleblock. A comparison of FIGS. 4 and 5 reveals that the combinedradar/communications system 130 (as the term is defined herein) does notinclude transmission antenna 110, reception antenna 116, radarmeasurements 128, communications data source 134 and receivedcommunications data 140, which are all indicated in FIG. 5 to beexternal to the combined radar/communications system 130.

The above-described common radar/communications system 130 may befurther enhanced by configuring the transmitted symbols to enable timetransfer and position determination during radar and/or communicationsoperations. New capabilities are added to the combined radar andcommunications operation through a set of processing blocks and a newpacket format. One aspect of the methodology is that each communicationsplatform is further configured to broadcast a signal that any othercommunications platform receiving the signal can use to synchronizesystem clocks to the set of master clocks among a selected subset oftransmitting platforms. This broadcast signal can occur during bothradar and communications operations. In addition, with three or moremobile or fixed platforms broadcasting the signal, any one receiving thesignal can also derive position information. The time transfer andposition determination service can operate at the same time as operationof both radar and communications functions. The broadcast information isderived from internal time and position information as determined by theindividual transmitting platforms. A small set of such platforms areconfigured to broadcast signals that transfer both accurate time andaccurate position to all other platforms within radiofrequency (RF)range.

An earlier section of this disclosure described how symbols areorganized to form a combined radar and communications waveform thatenables both the radar and communications system to functionsimultaneously. Once it has been determined how symbols can betransmitted, traditional methods allow their combination into sets ofsymbols called a packet. FIG. 6A is a diagram representing the format ofa standard packet 200. Each standard packet 200 includes the followingdata in the order listed: a header 202, source data 204, destinationdata 206, error correction-coded payload data 208 and checksum data 210.From that basic item, a sequence of packets can be transmitted reliablyto one or many destinations and can thus form a communications network.This packet architecture comes in many specific forms made for specificprotocols, but shares a number of common attributes that are known topractitioners of the art of radio navigation. In a standard approach, toadd time and position information, a contiguous portion of the standardpacket is typically set aside for this information. While this would bea normal design choice, it would have several drawbacks.

The first drawback is that having a single contiguous time and positioninformation packet section does not allow fast enough updates under manyconditions where the transmitting platform is very dynamic in motion(and thus changing in position at a very fast rate in an unpredictablefashion). This is because the position could only be updated at thepacket rate, rather than the rate required by the dynamic rate of theplatform which might be much higher. Note that this is not a problem forGPS since the GPS satellites have known and tightly controlled orbitsand their position can be predicted far in advance.

The second drawback is that pulsed jamming could destroy detection ofthe entire time and position information if it occurred during thecontiguous time and position packet section.

The third drawback is that using such a normal packet section withsymbols chosen to meet the designed signal to noise ratio (SNR) onlyallows time and position information to be shared when thecommunications link meets the minimum SNR level for communications.However, a system must often be designed such that during GPS outageswhen the radar antenna is pointed in a completely different directionfrom other platforms in the network, it must still be possible tosupport continuous time transfer and position determination services.This means that the signal may only be detected in the lowest sidelobesof the antenna pattern and therefore the SNR may be much lower than theSNR for communications depending on the relationship between thepointing direction of the transmitting antenna and the receivingplatform's antenna.

In an attempt to solve all of the above-described problems attending astandard packet, this disclosure introduces the concept of asupersymbol. A supersymbol uses the phase terms, but does not change thechirp slopes. Thus T_(i)=T and only the phases {c_(i), γ_(i)} are used.This is because the chirp phase can be more accurately estimated. Thisis shown in FIG. 7 for a 1000-sample simulation involving a linear chirppulse model in which the linear phase-modulated signal is described byEq. (7), where a, b, c are parameters (hereinafter “coefficients”) of apolynomial function that control the chirp slope (a.k.a. chirp rate),initial frequency and initial phase of the chirp signal. FIG. 7 showsthe simulated errors for parameter a (solid line), parameter b (dashedline) and parameter c (dotted line).

The supersymbol is defined as follows in a channel with bandwidth B: Letthe up chirp start with a frequency f_(c)−B/2 at time 0 and then go to afrequency f_(c)+B/2 at time T; then the complementary down chirp willstart with a frequency f_(c)+B/2 at time T and end at a frequencyf_(c)−B/2 at time 2T. Thus the up and down chirps are equal in length.The two chirp slopes are represented by the values of parameters named aand α, and the two frequencies are represented by the values ofparameters named b and β. Their values can be related to the chirpparameters by a=B/T, b=f_(c)−B/2, α=−B/T, and β=f_(c)+B/2. The resultsare the following equations representing the two chirps of onesupersymbol:s _(up)(t)=exp(2πj((B/T)t ²+(f _(c) −B/2)t+c)), 0≤t<Ts _(down)(t)=exp(2πj((−B/T)(t−T)²+(f _(c) +B/2)(t−T)+γ)), T≤t<2THere −½<c, γ<½. Then the supersymbol S(t) of length m is defined as theconcatenation of m pairs of up and down chirps with identical up anddown phases c and γ as:S(t)=[s _(up)(t)₁ , s _(down)(t)₁ , s _(up)(t)₂ , s _(down)(t)₂ , . . ., s _(up)(t)_(m) , s _(down)(t)_(m)]Then the packet is formed by including multiple pairs of contiguoussections made up of supersymbols (referred to hereinafter as “timingheader/position prediction slots”), which timing header/positionprediction slots occur at a rate defined by the platform dynamics. Eachposition prediction section may include one or more supersymbols. Eachtiming header also is made up of supersymbols. When a supersymbol oflength m is used, the length can be adjusted to meet much lower SNRrequirements than the communications channel.

The symbol error as a function of supersymbol length is illustrated inFIG. 8, which graph depicts results of a computer simulation of theprobability of symbol error versus relative SNR (dB) for differentsupersymbol lengths. This graph shows how moving from a high multiphaseshift-keyed (MPSK) modulation symbol (such as might be used forhigh-data-rate communications) having 64 MPSK modulation phases persymbol (M=64) down to a binary phase shift-keyed (BPSK) modulationsymbol having two phases per symbol (M=2) produces an improvement in theSNR of 26 dB. Further improvements to the SNR can be achieved byincreasing the symbol length m. FIG. 8 shows the symbol error as afunction of lengthening of the symbols by factors of 2 (that is, keepingthe modulation type BPSK and lengthening the symbols by factors of 2).Each increment in symbol length causes a similar improvement of anadditional 6 dB. This is indicated in FIG. 8 by curve labels in the formBPSK/2^(i), which means that the denominator is 2 to the i-th power,where i in an integer that varies from 0 to 6 in FIG. 8. Thus theoperation of the time transfer and position determination services canbe pushed down by 20, 30, even 50 dB SNR in extreme cases as compared tothe communications SNR.

The up and down phases of the supersymbols in each position predictionsection in a packet are varied from one position prediction section to anext position prediction section to represent respective positionpredictions for the combined radar/communications system which werevalid for respective durations of the associated (contiguous) timingheaders included in the packet. In the case wherein a positionprediction is associated with a timing header, the combined informationprovides a predicted position of a transmitting platform which was validfor the duration of the timing header transmission.

FIG. 6B is a diagram representing the format of one example of anenhanced packet 220 containing four timing headers 222 a-222 d made upof supersymbols and four position prediction sections 224 a-224 d alsomade up of supersymbols. Each contiguous timing header and positionprediction section with position prediction forms a respective timingheader/position prediction (THPP) slot. The number of THPP slots in anenhanced packet 220 may be different than four. Depending on whether theenhanced packet 220 is being transmitted or received, the timing header222 a will start at time T₀ using the transmit clock or time T₁ usingthe receive clock. In accordance with the format depicted in FIG. 6B:position prediction section 224 a is contiguous with timing header 222a; position prediction section 224 b is contiguous with timing header222 b; position prediction section 224 c is contiguous with timingheader 222 c; and position prediction section 224 d is contiguous withtiming header 222 d. Each of the position prediction sections 224 a-224d can have one or more supersymbols. It should be appreciated that thetiming header 222 a (see FIG. 6B) that replaces the standard header 202(see FIG. 6A) at the start of the packet is made up of supersymbols. Thepurpose of constructing a timing header using supersymbols is describedbelow.

The enhanced packet 220 depicted in FIG. 6B further includes: sourcedata 204 contiguous with position prediction section 224 a; destinationdata 206 contiguous with source data 204; error correction-coded payloaddata 230 a between destination data 206 and timing header 222 b; errorcorrection-coded payload data 230 b between position prediction section224 b and timing header 222 c; error correction-coded payload data 230 cbetween position prediction section 224 c and timing header 222 d; anderror correction-coded payload data 230 d between position predictionsection 224 d and the checksum data 210 at the end of the enhancedpacket 220. The lengths of the packet sections shown in FIG. 6B are notdrawn to scale, meaning that the depicted lengths are not intended torepresent the number of bits of data contained in each section. Forexample, the packet sections containing payload data may contain morebits of data

FIG. 9 is a block diagram identifying some components of a time transferand position determination system in accordance with one embodimentwhich has been added to (and may be incorporated in) the combinedradar/communications system 130. In this example, the combinedradar/communications system 130 transmits signals using a fixedtransmission antenna 110 and receives signals using a fixed receptionantenna 116. Each receiving platform may be configured as shown in FIG.9 to receive time and position information from at least three similarlyconfigured transmitting platforms and then use that broadcastinformation to calculate the time and position of the receivingplatform.

FIG. 17A is a diagram showing four radar systems 48 a-48 d respectivelymounted on aircraft 46 a-46 d. Assume that the four radar systems 48a-48 d are all operating concurrently while the aircraft 46 a-46 d aremoving along their respective flight paths. More specifically, it isassumed that radar systems 48 b, 48 c and 48 d are broadcasting signalscontaining time and position information for each aircraft. For example,the time and position information broadcast by the radar system 48 bonboard aircraft 46 b specifies the position of aircraft 46 b at a firstspecified time. Likewise the time and position information broadcast bythe radar system 48 c onboard aircraft 46 c specifies the position ofaircraft 46 c at a second specified time. Similarly, the time andposition information broadcast by the radar system 48 d onboard aircraft46 d specifies the position of aircraft 46 d at a third specified time.The arrows in FIG. 17A indicate that these broadcast signals are beingreceived by the radar system 48 a onboard the aircraft 46 a. A computersystem onboard the aircraft 46 a is configured to compute the localposition and time offset of the radar system 48 a using the timing andposition information received from the radar systems 48 b-48 d. The timeoffset is used to adjust a local clock onboard the aircraft 46 a. Thecomputed local position of aircraft 46 a may be used to compute thedistance separating aircraft 46 a from any one of the other threeaircraft 46 b-46 d. With cooperating FMCW radar systems at knowndistances, some of these returns could be filtered using a demod/remodfilter, as will be described in more detail below with reference to FIG.17B.

Referring again to FIG. 9, communications data generated by acommunications data source 134, local position data 186 and timingheaders 222 are converted by a packetizing module 188 into enhancedpackets (hereinafter “packetized”) in accordance with the protocoldepicted in FIG. 6B. The packetized data output by the packetizingmodule 188 forms the transmit baseband input to the CRCW waveformgenerator 106′ (not shown in FIG. 9, but see FIG. 4) of the combinedradar/communications system 130. The CRCW waveform generator 106′converts the packetized data into CRCW-modulated signals which arebroadcast by the transmission antenna 110 of the platform.

The platform partly depicted in FIG. 9 also receives CRCW-modulatedsignals representing communications data broadcast by other platforms.The baseband communications signal processing module 138 (not shown inFIG. 9, but see FIG. 4) of the combined radar/communications system 130is configured to decode the digitals signals to form the receivebaseband output consisting of the set of symbols derived by thecommunications receiver that were received from the i-th transmittingplatform, including time and position information for the i-thtransmitting platform. The communications data 140 contained in theenhanced packets from the i-th transmitting platform is reconstructed bya de-packetizing module 190. Respective sets of communications data 140received from multiple transmitting platforms are stored in anon-transitory tangible computer-readable storage medium.

The platform depicted in FIG. 9 further includes modules for processingraw digitized baseband samples being processed in the combinedradar/communications system 130, which baseband samples are derived fromenhanced packets transmitted by and received from other platforms. Aspreviously described, the received enhanced packets contain informationregarding the predicted positions of other transmitting platforms whichare valid for the duration of the respective timing headertransmissions. The modules for processing baseband samples include atiming correlation module 192 which uses correlation (described indetail below) to extract the timing information t_(i) (i=1, 2, . . . ,m, where m≥3) from respective timing headers received from the mtransmitting platforms. The modules for processing baseband samplesfurther include a position demodulation module 194 which usesdemodulation to extract the position information x_(i) (i=1, 2, . . . ,m) from respective position predictions received from the m transmittingplatforms. The timing and position information (x₁, t₁), . . . , (x_(i),t_(i)), . . . , (x_(m), t_(m)) is then processed by time and positioncalculation module 196, which is configured to compute the localposition and time offset of the receiving platform using the timing andposition information received from at least three transmittingplatforms. The local position data 186 is then included in subsequenttransmissions by the combined radar/communications system 130, while thetime offset is used to adjust the local clock 198.

For ease of comparison, FIG. 9 depicts modules 188, 190, 192, 194 and196 which are external to the combined radar/communications system 130.However, all of these modules are preferably incorporated inside thecombined radar/communications system 130 for the purpose of creating anenhanced combined radar/communications system 130.

The process for a receiving platform to estimate its own time andposition from the information in an enhanced packet will now bedescribed. For completeness, a standard process is described below whichany receiving platform may use to estimate its position and time byreceiving time and position information from a set of n platforms allbroadcasting enhanced packets using the methodology described herein.

The first pieces of information that each receiver must receive are theupdated positions of all n transmitting platforms. This comes in theform of a position prediction valid during the timing headertransmission. In particular, every position prediction is a set of Dbits sent in a position prediction section of an enhanced packet 220,corresponding to a standard constant acceleration motion equation:r _(ij)(t)=r _(0ij) +r _(1ij) t+r _(2ij) t ²/2, 0<t<THwhere r_(ij)(0) is the position at time TH₀ when the previous timingheader was transmitted. Here r, r₀, r₁ and r₂ are three-dimensionalvectors. Each vector has x, y, z components, with this equationrepresenting motion of the i-th transmitting platform, and j is the slotindex of the j-th such position prediction section within the packet asshown in FIG. 6B (e.g., position prediction section 224 c is the thirdposition prediction section from the start of the enhanced packet 220,in which instance j=3). As previously noted, each packet portionconsisting of a timing header (in the form of supersymbols) and acontiguous position prediction section (also in the form ofsupersymbols) is referred to herein as a THPP slot, so that the j-thposition prediction section is part of the j-th THPP slot. Note thatother types of motion equations and even more complicated or simplermotion models are equally possible to support. Here the information sentin the j-th THPP slot of the enhanced packet would contain the x, y, zcoordinates of each vector r₀, r₁, r₂ (or an equivalent form of theequation) as well as the time TH₀. The motion equation is valid over itsj-th corresponding header transmission time (TH) on the transmittingplatform and every position period PP the timing header and motionequations are retransmitted during the total enhanced packettransmission time. This allows more frequent position and time updates,required when platforms are moving unpredictably (unlike GPS satelliteswhose motion can be predicted years in advance).

The second piece of information that each receiver must estimate is thetime of arrival of the timing header from each transmitting platform toa receiving platform. The j-th timing header (as shown in FIG. 6B) issent out at time H_(j) according to the transmitter clock from all ofthe transmitting platforms. This timing header consists of a sequence ofsupersymbols with good autocorrelation properties. The sequence could bethe same across all platforms within the common timing and positionnetwork. Or the sequence could be specific to each platform. In thelatter case, the sequence must be communicated to all otherparticipating platforms. Hence the latter type of operation requiresmore complexity and overhead than simply using a single agreed-uponsequence. This disclosure henceforth assumes that the sequence is thesame across the network; thus the time duration TH is also known.Standard sequences with good autocorrelation properties are the Barkercodes as shown in Table 1 below.

TABLE 1 Sidelobe Level Length Codes Ratio (dB) 2 +1 −1 −6 3 +1 +1 −1−9.5 4 +1 +1 −1 +1 −12 5 +1 +1 +1 −1 +1 −14 7 +1 +1 +1 −1 −1 +1 −1 −16.911 +1 +1 +1 −1 −1 −1 +1 −1 −1 +1 −1 −20.8 13 +1 +1 +1 +1 +1 −1 −1 +1 +1−1 +1 −1 +1 −22.3

For longer sequences, one can use maximum length sequences, which are atype of pseudorandom binary sequence. Note that the received sequence iscorrelated against the known sequence to measure the relative time delayof the timing header between remote transmitting and local receivingclocks. The final clock time that is used for setting the local time isbased on this relative time delay together with the remote clock time(TH₀) communicated within the THPP slot. This aspect is described inmore detail below.

The timing header arrives at a receiving platform i at some later timeh_(ji) according to the receiving clock. The time delayt_(ij)=h_(ij)−H_(j) depends on the distance and propagation velocity, aswell as the receiver clock offset, which is unknown. Note that this isdifferent from GPS in that the signals from each satellite beingcorrelated are unique to that satellite. In the system disclosed herein,each signal occupies a different frequency band. By having a singleknown timing header, new transmitting platforms can join theposition/timing network at will (unlike the GPS satellite system whereall the satellite information must be known a priori). Succeeding timingheaders and position predictions in the packet are handled in the samemanner.

The standard “GPS” equations allow a solution for both time and positionof the receiving platform as follows. Let c be the RF propagationvelocity (speed of light in the medium under consideration). Then thefollowing equations must be solved for each of the j THPP slots:|a _(j) −x _(ij) |+b _(j) =ct _(i) , i=1, 2, . . . n.Here a_(j)=(a₁, a₂, . . . , a_(d))^(T) is the (unknown) position vectorof the receiving platform (in d dimensions, which is typically d=3);x_(ij)=r_(ij)(TH/2) is the position vector of the i-th transmittingplatform at the center time of timing header transmission for the j-thTHPP slot within the enhanced packet 220; and b is the unknown time(clock) offset. By sending the motion model, this can also be used tocompute the Doppler frequency during each timing header transmission andhence to get a better correlation and time of arrival. These equationscan be solved either by iteration or directly or by using a combinationof iteration and direct solution. For the purpose of illustration, adirect method is described in what follows. The index j is dropped sincethe processing is identical for all of the THPP slots.

Moving b to the other side of the equation and squaring gives:a ^(T) a−2x _(i) ^(T) a+x _(i) ^(T) x _(i)=(ct _(i))²−2b(ct _(i))+b ².Rearranging this equation gives:x _(i) ^(T) a−b(ct _(i))=(a ^(T) a−b ²)/2+(x _(i) ^(T) x _(i)−(ct_(i))²)/2.Define the following matrix:

$\beta = \begin{pmatrix}1 & 0 & \ldots & 0 \\0 & 1 & \ldots & 0 \\\vdots & \vdots & \ddots & 0 \\0 & 0 & \ldots & {- 1}\end{pmatrix}$Then the vector z=(a, b)^(T) of unknowns satisfies the followingequation:z ^(T)β_(z) =a ^(T) a−b ²and h_(i)=(x_(i),ct_(i))^(T) satisfies the following equation:h _(i) ^(T) βh _(i) =x _(i) ^(T) x _(i)−(ct _(i))².This gives:h _(i) ^(T) βz==z ^(T) βz/2+h _(i) ^(T) βh _(i)/2.Set the matrix H=(h₁ ^(T), h₂ ^(T), . . . , h_(n) ^(T))^(T) and thescalar unknown λ=z^(T) βz/2. Set u=(H^(T))⁻¹ (1, 1, . . . , 1)^(T) andv=(H ^(T))⁻¹(h ₁ ^(T) βh ₁ , h ₂ ^(T) βh ₂ , . . . , h _(n) ^(T) βh_(n))^(T)/2.Thenβz=λu+vandλ=z ^(T) βz/2are two equations both satisfied by the unknown λ. Solving yields:z ^(T) βz=(λu+v)^(T)β(λu+v)=2λor(u ^(T) βu)λ²+2(u ^(T) βv−1)λ+(v ^(T) βv)=0which is a quadratic equation in λ. Then the unknowns a and b can besolved using the following equation:

$\begin{pmatrix}a \\b\end{pmatrix} = {z = {{\lambda u} + v}}$This result gives both the position of the receiver a and the timeoffset b (so that its clock can be adjusted). Note that there may be twosolutions for the quadratic equation, yielding two different possibleposition for a. This ambiguity can be resolved based on previouspositions. Note that the time offset b is the time difference betweenthe remote clock and the local clock for the current timing header. Toset/update the local clock with the actual synchronized time, the clocktime TH₀ included in the THPP slot is used together with this timeoffset b.

FIG. 10 is a block diagram identifying some components of a timetransfer and position determination system in accordance with anotherembodiment which has been added to (and may be incorporated in) acombined radar/communications system 130 that transmits and receivessignals using steerable antennas instead of fixed antennas as shown inFIG. 9. The system depicted in FIG. 10 further differs from the systemdepicted in FIG. 9 by the addition of a beam steering controller 184.The beam steering controller 184 comprises a processor or computer thatis configured (e.g., programmed) to compute a steering vector thatcontrols the directions of the steerable antennas based on a steeringangle received from a system controller (not shown in FIG. 10) of thecombined radar/communications system 130. The steering angle is selectedto facilitate the transmission of signals in a particular directionusing a steerable transmission antenna 110′ and the reception of signalsfrom that particular direction using a steerable reception antenna 116′.

In accordance with a further aspect of the methodology disclosed herein,performance is optionally enhanced through the use of intentional beamjitter. More specifically, sidelobe operation of the time/positionservice (as well as the communications service or any other signalservice taking place through the sidelobes of the antenna pattern) isenhanced using intentional beam jitter. For example, during operation ofa radar system while using the sidelobes of the beam pattern tocommunicate with other platforms (including the time/position servicebeing described), the signal being received through the sidelobes ismuch weaker than the signal of the mainbeam (a.k.a., main lobe).

FIG. 11 is a block diagram identifying the same components identified inFIG. 10, but with the addition of a beam jitter subsystem 250 inaccordance with a further embodiment. This beam jitter subsystem 250 isconfigured to intentionally apply angle jitter to the steerabletransmission antenna 110′ to enhance performance as described in theimmediately preceding paragraph.

To provide a specific example, it will be assumed that the type ofantenna being used is a uniform linear array, but any other type ofantenna that can be rapidly and dynamically pointed to a desireddirection can be used. FIG. 12 shows an example of an antenna radiationpattern in polar form for a vertical uniform linear array with fourelements with 0-degree boresight pointing angle with a ground plane thateliminates any backside radiation.

More generally, FIG. 13 shows the pattern of various uniform lineararrays having a number of elements in a range from 4 to 256, showing howthe beam width and sidelobes vary with array size and plotted inrectangular coordinates. As seen in FIG. 13, the sidelobes can impactthe SNR by 40 or 50 dB or more compared to the mainbeam. What is evenworse is that for many azimuth angles, the pattern has nulls and dropsrapidly in power, creating situations where badly placed platforms mayhave a much worse SNR than even the typical sidelobe level at certainangular locations. For example, with a uniform linear array of 64elements, the distribution of SNR relative to the mainbeam is shown inFIG. 14. In this figure, almost half of the spatial angles have relativeSNRs below −40 dB, with over 2% of the angles having a relative SNRimpact of more than 70 dB.

Intentional beam jitter solves this problem by increasing the minimumSNR rather than having “nulls” in the signal coverage. The effect is toslightly reduce the mainbeam power; this can be balanced by choosing thejitter angle sequence appropriately. Beam jitter uses a clock that is Jtimes faster than the sample clock for the transmitter and receiver. Theinteger J≥2 is chosen to meet system requirements; common values are 2or 3.

FIG. 15 is a block diagram identifying components of a beam jittersubsystem 250 that is added to (and may be incorporated in) a combinedradar/communications system 130. However, this same approach can be usedin any sidelobe broadcast of a signal where SNR control is desired.

As depicted in FIG. 15, the system controller of the combinedradar/communications system 130 generates a commanded steering angle ϕ.representing the desired direction of the steerable transmission antenna110′. This commanded steering angle ϕ is intentionally altered usingbeam jitter calculated to enhance performance of the overall system. Thecombined radar/communications system 130 also communicates with a jitterangle subsystem controller 254, sending commands to point the beam tospecified angles based on system needs, such as tracking friend or foeor scanning. Both the transmitter antenna beam and receiver antenna beammust be jittered to ensure that their respective antenna nulls are notat the angle of the other antenna.

In accordance with one embodiment, the beam jitter subsystem 250operates as follows. The jitter angle subsystem controller 254 loads thedesired antenna jitter angle sequence 256 at the beginning of eachoperation. At each clock signal of frequency F_(s) (the sample rate)from the sample clock 258, a modulo operator 260 computes k=mod(j, J),meaning that the modulo operator 260 finds the remainder k afterdivision of number j by the number J. The next jitter angle ϕ₀=a_(k)from the antenna jitter angle sequence {a₀, a₁, . . . , a_(k), . . . ,a_(J-1)} is chosen at a rate of J*F_(s) by a jitter angle setting module262 and then added to the commanded steering angle ϕ by a summer 252.The sum ϕ+ϕ₀ output by summer 252 is then used by the beam steeringcontroller 184 to compute a steering vector that controls the directionof the steerable transmission antenna 110′. The beam steering controller184 computes a steering vector that controls the direction of thesteerable reception antenna 116′ in a similar manner. The pointing anglethus changes at a rate J times the sample rate F_(s) of the transmitterand receiver, causing an averaging effect on each sample.

The performance improvement due to intentional beam jitter is shown inFIGS. 16A-16D for uniform linear arrays having a respective number ofelements equal to 4, 16, 64 and 256 with J=3. A system designer wouldchoose the angle sequence based on the performance given by such asimulation based on the actual antenna response. The angle sequence usedin FIGS. 16A-16D is {−a, 0, a}, where the value of a is the x-axis valuelabeled “Jitter Angle” (jitter angle is in degrees in FIGS. 16A-16D).Alternative sequences could be {−a, a} with J=2 or even longer sequencesdepending on the desired performance. The system designer would weighthe improvement in minimum SNR over the mainbeam loss and choose anappropriate level of jitter. For example, with a uniform linear arrayincluding 64 elements, one could achieve a 27-dB improvement in minimumSNR at the expense of a 0.5-dB loss in mainbeam performance with ajitter sequence of {−0.4°, 0°, 0.4°} (see FIG. 16C).

A combined radar/communications system configured as described above hasthe following advantageous features: (1) time transfer and positiondetermination are enabled by the broadcast of signals; (2) the timetransfer and position determination services can operate at the sametime as operation of either or both radar and communications functions;(3) the time transfer and position determination services can operate atmuch lower signal-to-noise levels (i.e., at much greater ranges) thanthe communications functions; (4) platforms can easily join or leave thetiming and position network due to operation on different frequencies;and (5) further improvements in signal coverage can be achieved throughintentional beam jitter. These features may be employed beneficially inmany RF applications for networks of platforms that require both radarand communications functions.

The foregoing features provide benefits for many cross-platformapplications that require simultaneous radar and communications. Forexample, the principles of operation described above may be employed inapplications involving wide-band signal generation that can be appliedto software-defined radio systems, satellite and ground communicationssystems and radar systems.

If FMCW radar systems are operated at the same frequency with the samechirp slopes, each radar system can interfere with every other radarsystem. In accordance with one embodiment of the method proposed herein,a three-step technique is used to significantly reduce suchinterference: (1) synchronize the time and frequency of all cooperatingradar systems; (2) allocate pulse start times for each radar system; and(3) use a demod/remod filter to reduce chirp interference fromcross-radar interference.

The first step to reduce interference is to create cooperative operationof the FMCW radar systems by requiring that all radar systems besynchronized in time and frequency (of transmission). This can be donethrough one of several techniques:

Each platform has clocks that are sufficiently stable that they remainsynchronized throughout the radar operation.

Each platform synchronizes its own clock using GPS.

Each platform synchronizes its own clock using the time and positionservice implemented as described previously herein. This produces timeoffsets between the local clock of each radar and the synchronized timecomputed from the master radar's enhanced message packets. This sequenceof time offsets is used to adjust the local clock frequency so thatfuture time offsets are driven to very small values.

The synchronization of each of the radar systems allows both thetransmission time of each transmitted chirp (or communications symbol)or chirp pair (see FIG. 2A) and the transmission frequencies to beprecisely controlled across all platforms within this cooperative FMCWnetwork. This synchronization by itself does not eliminate thecross-radar interference, but subsequent processing of the interferingreturns is configured to constrain the interfering returns so that thereturn delays have specific interpretations. A simple case depicted inFIG. 17B is used to illustrate this point. Note that the propagationdelay d corresponding to a range R is d=R/v_(c), where v_(c) is thevelocity of the RF signals.

FIG. 17B shows four radar returns for two radar systems 48 a and 48 b(one mounted on an aircraft 46 a and the other mounted on an aircraft 46b) which are both operating at the same time while aircraft 46 a and 46b are moving along respective flight paths. Three of the four radarreturns depicted in FIG. 17B are seen by radar system 48 a. Suppose thatboth radar systems 48 a and 48 b are synchronized and transmitrespective FMCW pulses at the same time at the same frequency and samechirp slope. Then the return delays of the four radar returns areinterpreted as follows:

The first FMCW pulse transmitted from radar system 48 a (onboardaircraft 46 a) is reflected off of object 50 a after a delay d₁₁ and areturn signal is reflected back to radar system 48 a after a furtherdelay d₁₁, resulting in a return delay of 2d₁₁ subsequent totransmission of the first FMCW pulse. The return delay of 2d₁₁corresponds to twice the range R₁₁ to object 50 a, i.e., d₁₁=R₁₁/v_(c).

The second FMCW pulse transmitted directly from radar system 48 b(onboard aircraft 46 b) to radar system 48 a at the same time when thefirst FMCW pulse was transmitted has an apparent delay of d₂₁=R₂₁/v_(c),where R₂₁ is the range from radar system 48 a to radar system 48 b.

In addition, the second FMCW pulse transmitted from radar system 48 b isreflected off of object 50 b after a delay d₂₂ and a return signal isreflected to radar system 48 a after a further delay d₁₂, resulting inan apparent delay (from the vantage point of radar system 48 a) ofd₁₂+d₂₂=(R₁₂+R₂₂)/v_(c) where R₁₂ is the range from radar system 48 a toobject 50 b and R₂₂ is the range from radar system 48 b to object 50 b.

Lastly, the second FMCW pulse transmitted from radar system 48 b isreflected off of object 50 b after a delay d₂₂ and a return signal isreflected back to radar system 48 b after a further delay d₂₂, resultingin a return delay (from the vantage point of radar system 48 b) of 2d₂₂,where d₂₂=R₂₂/v_(c) where R₂₂ is the range from radar system 48 b toobject 50 b.

Thus, the radar system 48 a onboard aircraft 46 a sees three returns atdelays 2d₁₁, d₂₁ and d₁₂+d₂₂, only one of which is a direct reflectionof the first pulse transmitted by radar system 48 a back to radar system48 a. The other two “fake” returns come through the sidelobes of radarsystem 48 a, but can have significant power, even as much power as thedirect return with delay 2d₁₁. Even though the d₂₁ return could befiltered out using a notch filter since the range between the platformsis known, the return d₁₂+d₂₂ could not be filtered out because the rangeto object 50 b is unknown. Using notch filters in that manner would alsocause blind ranges when objects of interest have the same range as otherradar systems, and thus would be undesirable. In general, each radarsystem could have many possible other returns (both direct and indirect)from the N−1 other radar systems and other reflecting objects.

The second step is to allocate pulse start times across the Ncooperating FMCW radar systems. Let the maximum return range be R_(max)so that d_(max)=2R_(max)/v_(c) is the maximum delay. Then if radarsystem 48 b delayed its pulse start time by d_(max); d₂₁ would becomed₂₁+d_(max) and d₁₂+d₂₂ would become d₁₂+d₂₂+d_(max) as seen by radarsystem 48 a while d₁₁ would remain unchanged. Thus the other returnswould fall outside of the return delay range [0; d_(max)] for radarsystem 48 a and so would be ignored by a low (high) pass frequencyfilter for up (down) chirps tied to the frequency range corresponding tothis delay range. Thus, a notch filter is not necessary as well.

What is described above only applies when each radar system is sending achirp with the same frequency and chirp slope at a given symbol time.When different symbols are transmitted having different chirp slopes,interference is caused when the interfering returned chirp is mixed witha chirp of a different rate, causing a chirped interfering signal with arate being the difference of the two chirp slopes. This is a wide-bandinterfering signal in the receiver that cannot be easily filtered out inthe frequency domain. To solve this problem, the methodology proposedherein includes the third step, which is to employ a demod/remod filterthat reduces the chirp interference due to cross-radar interference byfirst demodulating all possible chirped symbols except the current onefor the receiver and subtracting out the sum of all the chirps detectedbefore proceeding with the frequency filter.

In more detail, each cooperative FMCW radar receiver operates asfollows:

(1) Using the communications network among the set of N cooperating FMCWradar systems, time and frequency are synchronized across the network ofradar systems.

(2) The pulse start time (hereinafter “symbol time”) is allocated acrossthe network based on radar identification. For simplicity, suppose theradar systems are respectively numbered j=1, 2, . . . , N. Then thestart time for radar system j will be t_(j)=(j−1)*d_(max). This assumesthat the symbol time 2T>Nd_(max). FIG. 18 shows these start timestogether with the respective time delay range td_(j) for each radarsystem j (which delay ranges are assumed to all have a length d_(max)).

(3) The return signal is received by a radar system and then mixed withthe transmitted chirp signal. As depicted in FIG. 19, the receptionantenna 116 receives RF electromagnetic waves 114 reflected from theradar target 102. The electrical signals from the reception antenna 116are amplified by low-noise reception amplifier 118. The frequency mixer120 then mixes the received signals with the transmitted signalsgenerated by the VCO 107 to produce first demodulated signals thatcontain phase information. The low-pass filter 122 performs low-passfiltering to obtain beat frequency signals which are sampled andconverted into digital signals. After low pass filtering andanalog-to-digital conversion, the digital samples pass through ademod/remod filter 72 to reduce interference due to signals receivedfrom other radar systems.

The demod/remod filter 72 attempts to detect (demodulate) everyinterfering chirped signal and then recreate each one at the correctamplitude and phase (remodulate) and subtract them out from the receivedsignal. The demod/remod filter 72 does this by mixing (multiplying) thereceived signal (digitized by the analog-to-digital converter 124 shownin FIG. 19) by the conjugate of each non-selected (non-used) chirpedsymbol having non-selected chirp slopes a_(j) and averaging theresulting output (producing an average “amplitude”) and multiplying thegenerated chirp by this value to produce a recreated chirp that issubtracted from the received signal. All of the non-used chirps can bedetected, generated and subtracted out in parallel.

The communications transmission system 76 identified in FIG. 19 includesthe digital modulation symbol generator 136 identified in FIG. 4. Thatsymbol generator outputs the slope and length of the selected symbolused in the transmit communication to an allowed symbol slopes module174, which stores information defining the sets of allowed symbol slopesin a non-transitory tangible computer-readable storage medium. Theallowed symbol slopes not selected by communications transmission system76 are output to the demod/remod filter 72. The allowed symbol slopesselected by communications transmission system 76 are output to theup/down ramp controller 104.

Still referring to FIG. 19, a time, frequency and position processingmodule 78 is configured to compute the local position and time offset ofthe combined radar/communications system using the timing and positioninformation received by the communications reception system 74. Thelocal position data is included in the packet of data transmitted by thecommon radar/communications transmitter 131. The time offset is used toadjust a system clock 80. The system clock 80 provides the symbol timeto up/down ramp controller 104 and a frequency reference to thevoltage-controlled oscillator 107.

FIG. 20 shows the operation of the demod/remod filter 72. Here thenon-selected chirp slopes 84 are used to generate chirps (step 86) whichare conjugated (step 90) and multiplied in mixer 92 with the digitizedsamples from the received signal. Then the average amplitude is computed(step 94). (The j-th box labeled “Average (Std)” denotes computing arunning average of non-selected chirp lengths corresponding to thenon-selected chirp slopes a_(j) together with a running variance of thatsame length. The output is updated when the variance is at a minimum.)The chirp generated in step 86 is then multiplied by the averageamplitude in mixer 88. These steps are performed in parallel for eachnon-selected chirp slope a_(j). The recreated chirps output from the setof mixers 88 are then summed by a summer 96. The summed chirps are thensubtracted from the received digitized samples (step 98 in FIG. 20) toproduce the output of the demod/remod filter 72 (hereinafter“demod/remod filter output”).

(4) Referring again to FIG. 19, the frequency content of the demod/remodfilter output is then estimated by a computation module 82 that usesFast Fourier transforms. The system then applies a low pass (high pass)frequency filter 176 based on the maximum return distance R_(max) andmaximum relative velocity V_(max) to pass all frequencies below

$g_{up} \geq {{\frac{2R_{\max}}{v_{c}} \cdot \frac{B}{T}} + \frac{2f_{c}V_{\max}}{v_{c}}}$for the up chirp and to pass all frequencies above

$g_{down} \leq {{{- \frac{2R_{\max}}{v_{c}}} \cdot \frac{B}{T}} + \frac{2f_{c}V_{\max}}{\nu_{c}}}$for the down chirp.

(5) A target return signal processing module 178 then finds each peak infrequency in the resulting filtered set of radar returns for the up anddown chirps and estimates both the relative range and velocity of theradar target 102 for each return using standard FMCW processingtechniques. Those radar measurements are then reported to the systemcontroller of the combined radar/communications system.

For the purpose of testing, a computer may be programmed to simulate thespectral performance of two platforms, each seeing the other's directsidelobe or indirect ground return at the same distances for oneparticular example scenario. One such simulation showed that a 15-dBreduction in peak matched power was related to the relative differencebetween chirp slopes ΔBW, the symbol time T and the sample rate f_(s) asΔBW·f_(s)/2T. This reduction is reduced even further through thedemod/remod filtering step. Using the demod/remod filter, the resultingchirp interference can be largely eliminated.

The technology disclosed in some detail above solves the problem ofsimultaneous radar operation across multiple platforms using the same RFspectrum. Using this technology, two or more radar systems do not haveto occupy different RF bands in order to not interfere with each other.And the radar systems do not have to restrict their performance to asubset of their operational bandwidth, since they can all use the samefull bandwidth. The technology disclosed herein also allows simultaneouscommunications across this network of radar platforms using the sametransmitted signal.

A combined radar/communications system configured as described above hasthe following advantageous features: (1) Simultaneous FMCW operationfrom multiple dispersed nodes or platforms using the same RF spectrum isenabled. (2) Interplatform interference is reduced through time andfrequency synchronization as well as controlling the pulse start timesand using demod/remod filtering to reduce cross-radar interference. (3)Benefits are provided from time transfer and position determinationthrough a broadcast signal using the same radar signal. (4) Simultaneouscommunications can also be supported in this mode. These features may beemployed beneficially in many radar sensor networks that benefit fromsimultaneous FMCW radar operation.

The processing of the waveform by the communications receiver (theuppermost processing path in FIG. 4) requires detecting each symbolreceived, which in the instant case means detecting the symbol frequencyslopes and phases for both the first and second symbol chirps. Thisprocess is shown in FIG. 21. The process may use any method to computeestimates of chirp slope (a) and initial phase (c) (recall that theparameter b need not be estimated unless an estimate of Dopplerfrequency is desired), but a streaming method is preferable to reduceprocessing latency and storage. One such method is described in U.S.patent application Ser. No. 15/652,027. The method in its simple formtakes as input a sampled form of a received signal and providesalgorithms that do two things: (1) the method detects when linearphase-modulated signals are present using a calculated metric value (themetric is denoted by d in U.S. patent application Ser. No. 15/652,027;and (2) the method estimates three fixed parameters (see parameters a,b, c in Eq. (9) below) in the linear phase-modulated signal. The linearphase-modulated signal is described by the equation:s(t)=e ^(2πj(at) ² ^(+bt+c))  (9)where t varies over time and a, b, c are parameters (hereinafter“coefficients”) of a polynomial function that control the chirp slope(a.k.a. chirp rate), initial frequency and initial phase of the chirpsignal. One can use parts of the methodology disclosed in U.S. patentapplication Ser. No. 15/652,027 to estimate the slope coefficient a andthe phase coefficient c and in turn reliably detect the CRCW symbolsbeing transmitted. The method of symbol detection for CRCW will bedescribed in some detail below. However, there are other additionalaspects to the design of a communications receiver which will not bedescribed in detail because such details are well known to personsskilled in the art. This disclosure will focus on the reception anddetection of the symbols being received in a CRCW receiver. Theprocessing steps to estimate a and c are as follows.

First, a mixed and down-converted sampled data signal {s_(n)} comes intothe baseband communications signal processing module 138 identified inFIG. 4. Then a phase estimate is done. If the incoming digital signal iscomplex valued, the phase can be computed as a tan 2(im, re), where thecomplex signal sample is of the form (re+i(im)). The function a tan 2( )is the arctangent function with two arguments. For any real number(e.g., floating point) arguments x and y not both equal to zero, a tan2(y, x) is the angle in radians between the positive x-axis of a planeand the point given by the coordinates (x, y) on it. There aresimplifications to calculating phase that are easier to implement inpractice than a full calculation of the a tan 2( ) function. Alternatemethods include: CORDIC (for COordinate Rotation Digital Computer, whichis a simple and efficient algorithm to calculate hyperbolic andtrigonometric functions, typically converging with one digit (or bit)per iteration), lookup tables and interpolation, and Chebyshevapproximation. These are not further described herein since they arewell known and standard. If, however, the incoming signal is real, theusual method to estimate phase involves using either a quadraturedemodulator or a Hilbert filter before calculating the phase. Thestructure and function of a quadrature demodulator is well known. See,for example, U.S. Pat. Nos. 5,426,669, 6,191,649 and 6,310,513. Thereare also well-known different ways to form an analytic (complex) signalusing a Hilbert filter. FIG. 21 shows one particular method 2 using aparallel delay and Hilbert filter approach before phase estimation. Thefinal step (after phase estimation) is to unwrap the raw phase value.

Referring to FIG. 21, the incoming signal is real. An analytic signal isformed using a Hilbert filter 24 and a matched delay 26 arranged inparallel. The matched delay 26 provides a delay that matches the delayproduced by the Hilbert filter 24. The delayed (real) and filtered(imaginary) signals are output in parallel to a phase estimator 28,which estimates the phases of the streaming signals. (Note that anormalized phase between −1 and 1 is used in what follows, rather than−π and π.) The signal phases output by phase estimator 28 are thenunwrapped by a phase unwrapper 30. (As used herein, the verb “to unwrap”means to add 2π for each complete cycle of the sinusoidal signal.)Unwrapping of phase can be done in several different standard ways. Acommon and simple approach is to do the following: given a phaseestimate θ and the previous phase sample θ₀, correct the phase estimateθ by adding multiples of ±2π (or ±1 if normalized) when (θ−θ₀) is lessthan −π (normalized −1) (respectively greater than it (normalized +1)).

Next, for each slope length of m=T_(i) for i=0, . . . , C−1, thefollowing iteration computes an estimate for a and c at each time stepn. Let Sy⁻¹=0 and Sxy⁻¹=0. Then iterating over the range n=0, . . . ,C−1 using the following equations gives final estimates â_(C-1) andĉ_(C-1) for parameters a and c in Eq. (9):Sy _(n) =Sy _(n-1)+θ_(n)−θ_(n-m)Sxy _(n) =Sxy _(n-1) −Sy _(n-1) +mθ _(n)â _(n) =â _(n-1) +A ₁(m)(−2Sxy _(n-1) +Sy _(n-1) +mθ _(n))+A ₂(m)(−Sy_(n-1) +mθ _(n))+A ₃(m)(θ_(n)−θ_(n-m))  (10)ĉ _(n) =ĉ _(n-1) +C ₁(m)(−2Sxy _(n-1) +Sy _(n-1) +mθ _(n))+C ₂(m)(−Sy_(n-1) +mθ _(n))+C ₃(m)(θ_(n)−θ_(n-m))  (11)Here the six values A₁(m)-A₃(m) and C₁(m)-C₃(m) are part of a 3×3 matrixM that is only dependent on the estimation window length m=T_(i) and canbe pre-computed for each chirp slope. The 3×3 matrix M is defined asfollows:

$M = {\begin{bmatrix}{\sum t_{i}^{4}} & {\sum t_{i}^{3}} & {\sum t_{i}^{2}} \\{\sum t_{i}^{3}} & {\sum t_{i}^{2}} & {\sum t_{i}} \\{\sum t_{i}^{2}} & {\sum t_{i}} & 1\end{bmatrix} = \begin{bmatrix}{A_{1}(m)} & {A_{2}(m)} & {A_{3}(m)} \\{\sum t_{i}^{3}} & {\sum t_{i}^{2}} & {\sum t_{i}} \\{C_{1}(m)} & {C_{2}(m)} & {C_{3}(m)}\end{bmatrix}}$Here the sums are over M consecutive samples of the phase and t_(i)denotes the relative times of the M samples and can be defined ast_(i)=i*f_(s). This approach comes from a direct application of ordinaryleast squares or linear regression.

FIGS. 22-24 are diagrams symbolically representing electronic circuitryfor respectively computing the values of three terms for estimating thechirp slope of the received signal (namely, the termsA₁(m)(−2Sxy_(n-1)+Sy_(n-1)+mθ_(n)), A₂(m)(−Sy_(n-1)+mθ_(n)) andA₃(m)(θ_(n)−θ_(n-m)) in Eq. (10)) implemented in a digital form that maybe instantiated in a field-programmable gate array (FPGA) or anapplication-specific integrated circuit (ASIC).

FIG. 22 shows an implementation 4 of a method for estimating the firstterm A₁(m)(−2Sxy_(n-1)+Sy_(n-1)+mθ_(n)) in Eq. (10). The notation usedin FIG. 22 (and in FIGS. 21 and 22) is as follows: Z⁻¹ denotes aregister or memory element which serves to delay a value by one clockperiod; the encircled “+” symbols denote a summer; and the encircled “x”symbols denote a multiplier. The phase estimate θ_(n) is inputted to amodule 10 that estimates the value of parameter Sy_(n-1). The module 10includes a delay buffer 12 which can be programmed for different delayvalues (up to some implementation-dependent maximum) where the delay isset equal to the slope length m. The phase estimate θ_(n) is alsoinputted to multiplier 16, which outputs the term mθ_(n) to a module 14that estimates the value of parameter −2Sxy_(n-1). The summer 18 addsthe estimated values output by module 10 and multiplier 16 to form thesum (Sy_(n-1)+mθ_(n)). The summer 20 then adds the estimated valueoutput by module 14 to the sum output by summer 18 to form the sum(−2Sxy_(n-1)+Sy_(n-1)+mθ_(n)). The multiplier 22 then multiplies the sumoutput by summer 20 and the value A₁(m) to produce a value for the firstterm A₁(m)(−2Sxy_(n-1)+Sy_(n-1)+mθ_(n)) in Eq. (10).

FIG. 23 shows an implementation 6 of a method for estimating the secondterm A₂(m)(−Sy_(n-1)+mθ_(n)) in Eq. (10). The phase estimate θ_(n) isinputted to a module 32 that estimates the value of parameter Sy_(n-1).The phase estimate θ_(n) is also inputted to multiplier 34, whichoutputs the term mθ_(n) to a summer 36. The summer 36 adds the estimatedvalues output by module 32 and multiplier 34 to form the sum(−Sy_(n-1)+mθ_(n)). The multiplier 38 then multiplies the sum output bysummer 36 and the value A₂(m) to produce a value for the second termA₂(m)(−Sy_(n-1)+mθ_(n)) in Eq. (10).

FIG. 24 shows an implementation 8 of a method for estimating the thirdterm A₃(m)(θ_(n)−θ_(n-m)) in Eq. (10). The phase estimate θ_(n) isinputted to a delay buffer 40 that delays the phase estimate by theslope length m. The phase estimate θ_(n) is also inputted to a summer 42which adds the incoming phase estimate to the negative value of thedelayed phase estimate output from delay buffer 40 to form the sum(θ_(n)−θ_(n-m)). The multiplier 44 then multiplies the sum output bysummer 42 and the value A₃(m) to produce a value for the third termA₃(m)(θ_(n)−θ_(n-m)) in Eq. (10).

FIG. 25 is a flowchart identifying steps of a method for basebandcommunications processing (performed by the baseband communicationssignal processing module 138 identified in FIG. 4) in accordance withone embodiment. The process partly depicted in FIG. 25 can generateparameter estimates using streaming (or on-the-fly) calculations andtherefore is suitable for FPGA or ASIC or other hardware-basedimplementation. In the following description, the term “block” refers toan electronic circuit embodied in hardware. The baseband communicationsprocessing depicted in FIG. 25 works as follows.

Each of the slope coefficient estimation blocks 52 that do thecalculations from Eq. (10) are labeled as a(T_(i)) in FIG. 25 andsimilarly for the phase coefficient estimation block 62 labeled asc(T_(i)) for Eq. (11). Only the references to A_(i)(m) in theimplementation figures (FIGS. 22-24) need to be changed to C_(i)(m) tocalculate c(T_(i)).

Then a set of delay buffers 54, each of length 2T−T_(i), is used to lineup the slope estimates for up and down chirps for each symbol i.Finally, symbol metric computation blocks 56 compute a symbol metricd_(i) for each such symbol slope using the following equation:

$d_{i} = {( {a_{i} - \frac{B}{T_{1}}} )^{2} + ( {a_{C\text{-}i} - \frac{B}{{2T} - T_{i}}} )^{2}}$

The smallest of the symbol metrics d_(i) is then chosen in block 58 andthat information is passed to both a symbol tracking block 60 and phasecoefficient estimation blocks 62 and 64 which estimate phasecoefficients c of each of the complementary chirps using Eq. (11). Thesymbol tracking block 60 identifies the time of the minimum value of thesymbol metric of the chosen chirp slope and, using a standard symboltime filter, produces a symbol sample time signal that is used byrespective symbol sampling blocks 66 and 68 to sample the phasescomputed from the phase coefficient estimation blocks 62 and 64. Lastly,the mapping block 70 takes the three identified values {a(T_(i)),c(T_(i)), c(2T−T_(i))} and from these values estimates the three indicesof the received symbol by computing i, j and l as follows:

$\{ {{i = \langle \frac{( {\frac{B}{a( T_{i} )} - T_{\min}} )}{( {C - 1} )} \rangle},{j = \langle \frac{D \cdot ( {{c( T_{i} )} + \pi} )}{2\pi} \rangle},{l = \langle \frac{D \cdot ( {{c( {{2T} - T_{i}} )} + \pi} )}{2\pi} \rangle}} \}$This triple of integers defines the received symbol. Here the angledbrackets denote rounding to the nearest integer.

Referring again to FIG. 4, the processing steps performed by the digitalmodulation symbol generator 136, which converts the communications datato symbols, will now be described in some detail. This processing blocktakes sequential sets of bits to be transmitted and converts them todigital values characterizing the symbols representing thecommunications data to be transmitted. It is very similar to how symbolsget mapped to (I, Q) constellations before modulation. If the values ofC and D are powers of 2, the main steps are as follows:

(1) Take a sequential set of K input bits, split the input bits intothree sets of log₂ K_(C), log₂ K_(D) and log₂ K_(D) bits;

(2) Map the first set to a chirp slope of the first chirp of each symbolby interpreting the bits as a number i from 0 to C−1 and then computeT _(i) =T _(min)+(T _(max) −T _(min))·i/C;

(3) Map the second set to an initial phase of the first chirp of thesymbol by interpreting the bits as a number j from 0 to D−1 and thencomputeΘ_(j)=−π+2π(j/D);

(4) Map the third set to an initial phase of the second chirp of thesymbol by interpreting the bits as a number l from 0 to D−1 and thencomputeΦ_(l)=−π+2π(l/D).These digital values are sent the combined radar/communications waveformgenerator 106′ (see FIG. 4), which produces a modulating signal that isfed to the VCO 107 to produce a final RF chirped signal with theappropriate slope and phases. If the values of C and D are not powers of2, this mapping can be accomplished through standard arithmetic codingtechniques, where the bits to be sent are encoded in base C·D² and theneach digit δ, 0≤δ<C·D², is associated with the symbol time T_(i) viaT _(i) =T _(min)+(T _(max) −T _(min))·└δ/D ² ┘/Cwhere └x┘ denotes the floor function, the greatest integer less than orequal to x.

The phases can then be found by setting δ_(r)=rem(δ, D²) (the remainderof dividing δ by D²). ThenΘ_(j)=−π+2π└δ_(r) /D┘/D

Similarly, set δ_(s)=rem(δ_(r), D) andΦ_(l)=−π+2π(δ_(s) /D).

There are a number of variants of the waveform and architecturedisclosed in detail above. For examples, this architecture could operateusing a direct RF conversion architecture (see FIG. 4) where theanalog-to-digital converter can be moved to directly after the low-noiseamplifier. The processing that follows the analog-to-digital converterwould then be digital instead of analog. This disclosure describes thecase where each transmitter uses its own frequency. This preventsinterference between two or more such systems. In alternativeembodiments, such systems could also multiplex their outputs so thatthis does not happen. This could be controlled by a higher levelprotocol. Alternatively, the two systems could use the same frequencyand through standard spread spectrum symbol coding, both could operateon the same frequency, but with greater mutual interference. Thespecific calculations described above with reference to FIG. 25 arebased on uniformly spaced chirp times and phases. If this is not thecase, the calculations would have to be modified via standardtechniques.

A method has been described for combining radar and communicationsfunctions using a set of common hardware and common signal processingtogether with a common waveform family. Linear frequency-modulatedsymbols are used to send communications at the same time that thesymbols are also used to measure range and range rate (or relativevelocity) of signal reflections off of multiple targets (as a radarwould do). In addition, radar detection and communications reception canbe done in a streaming fashion, so as to avoid additional latency. Bothrange, range rate and symbol values are produced every symbol period T.Thus there is no need for synchronization intervals or periods ofinactivity for either the radar or the communications system. This alsomeans that the waveform is ideal for point and shoot networkingapplications where packets are short in time and data synchronizationmeans inefficiency. The foregoing features provide benefits, includingsharing of antennas for both systems when applicable, reducing costassociated with interference (primarily radio frequency interference) oftwo such systems on a single platform, and reducing cost and complexityso that upgrades of both systems can be accomplished at the same timeand integration problems are taken care of in the design process.

Certain systems, apparatus, applications or processes have beendescribed herein as including a number of modules. A module may be aunit of distinct functionality that may be implemented in software,hardware, or combinations thereof, except for those modules which arepreferably implemented as hardware or firmware to enable streamingcalculations as disclosed herein. When the functionality of a module isperformed in any part through software, the module can include anon-transitory tangible computer-readable storage medium.

While systems and methods for enabling time transfer and positiondetermination in a combined radar/communications system and for enablingtwo or more dispersed platforms to simultaneously operate theirrespective FMCW radar systems using the same RF spectrum have beendescribed with reference to various embodiments, it will be understoodby those skilled in the art that various changes may be made andequivalents may be substituted for elements thereof without departingfrom the teachings herein. In addition, many modifications may be madeto adapt the concepts and reductions to practice disclosed herein to aparticular situation. Accordingly, it is intended that the subjectmatter covered by the claims not be limited to the disclosedembodiments.

The embodiments disclosed above use one or more processing or computingdevices. Such devices typically include a processor, processing device,or controller, such as a general-purpose central processing unit, amicrocontroller, a reduced instruction set computer processor, an ASIC,a programmable logic circuit, an FPGA, a digital signal processor,and/or any other circuit or processing device capable of executing thefunctions described herein. The methods described herein may be encodedas executable instructions embodied in a non-transitory tangiblecomputer-readable storage medium, including, without limitation, astorage device and/or a memory device. Such instructions, when executedby a processing device, cause the processing device to perform at leasta portion of the methods described herein. The above examples areexemplary only, and thus are not intended to limit in any way thedefinition and/or meaning of the terms “processor” and “computingdevice”.

The process claims set forth hereinafter should not be construed torequire that the steps recited therein be performed in alphabeticalorder (any alphabetical ordering in the claims is used solely for thepurpose of referencing previously recited steps) or in the order inwhich they are recited unless the claim language explicitly specifies orstates conditions indicating a particular order in which some or all ofthose steps are performed. Nor should the process claims be construed toexclude any portions of two or more steps being performed concurrentlyor alternatingly unless the claim language explicitly states a conditionthat precludes such an interpretation.

The invention claimed is:
 1. A combined radar/communications systemcomprising a common radar/communications transmitter having atransmission antenna and a combined radar and communications receiverhaving a common reception antenna, wherein the commonradar/communications transmitter is configured to transmit combinedradar/communications waveform-modulated signals representing packets ofdata, the data in each packet including payload sections made up ofmultiple symbols and timing header and position prediction slots made upof multiple supersymbols, wherein the payload sections and timing headerand position prediction slots alternate in sequence within the packet,and each timing header and position prediction slot includes arespective timing header and a respective position prediction sectionwhich is contiguous with the respective timing header.
 2. The combinedradar/communications system as recited in claim 1, wherein each symbolconsists of an up chirp and a down chirp, and each supersymbol consistsof a concatenation of pairs of up chirps and down chirps of equal chirplengths, the up chirps of the concatenation having the same up phase andthe down chirps of the concatenation having the same down phase.
 3. Thecombined radar/communications system as recited in claim 2, wherein: thesupersymbols in timing headers of the timing header and positionprediction slots are phase encoded with time information indicating aduration of time for which a prediction of the position of the combinedradar/communications system was valid; and the supersymbols in positionprediction sections of the timing header and position prediction slotsare phase encoded with position information indicating the prediction ofthe position of the combined radar/communications system.
 4. Thecombined radar/communications system as recited in claim 2, wherein theup and down phases of the supersymbols in each position predictionsection in a packet are varied from one position prediction section to anext position prediction section to represent respective positionpredictions for the combined radar/communications system which werevalid for respective durations of the respective contiguous timingheaders.
 5. The combined radar/communications system as recited in claim4, wherein the up and down phases of the supersymbols in each timingheader in a packet are varied from one timing header to a next timingheader to represent the respective durations of time for which therespective position predictions were valid.
 6. The combinedradar/communications system as recited in claim 4, wherein a positionprediction is associated with a timing header in each timing header andposition prediction slot, the combined information providing a predictedposition of the combined radar/communications system which was valid forthe duration of the timing header transmission.
 7. The combinedradar/communications system as recited in claim 1, further comprising: abeam steering controller configured to control a direction in which thetransmission antenna transmits signals in response to receipt of acommand representing a steering angle; and a beam jitter systemconfigured to generate the command by summing a signal representing ajitter angle to a signal representing a commanded steering angle.
 8. Thecombined radar/communications system as recited in claim 7, wherein thebeam jitter system is further configured to generate successive commandsby summing respective signals representing respective jitter angles of ajitter angle sequence to the signal representing the commanded steeringangle.
 9. The combined radar/communications system as recited in claim1, further comprising: a timing correlation module which is configuredto extract timing information from respective timing headers in packetsreceived from at least three transmitting platforms using correlation; aposition demodulation module which is configured to extract positioninformation from respective position predictions in the packets receivedfrom the at least three transmitting platforms using demodulation; and atime and position calculation module which is configured to compute thelocal position and time offset of the combined radar/communicationssystem using the timing and position information received from the atleast three transmitting platforms.
 10. The combinedradar/communications system as recited in claim 9, wherein the localposition data is included in the packet of data transmitted by thecommon radar/communications transmitter.
 11. The combinedradar/communications system as recited in claim 9, further comprising alocal clock, wherein the time offset is used to adjust the local clock.12. The combined radar/communications system as recited in claim 9,wherein the combined radar/communications system is installed on amobile platform.
 13. A method for determining a position of a mobileplatform, comprising: receiving timing and position information from atleast three transmitting platforms by way of a reception antenna onboardthe mobile platform; and computing a local position and a time offset ofthe mobile platform using the timing and position information receivedfrom the at least three transmitting platforms, wherein the timing andposition information is extracted from packets of data carried bycombined radar/communications waveform-modulated signals received fromthe at least three transmitting platforms, the data in each packetincluding payload sections made up of multiple symbols and timing headerand position prediction slots made up of multiple supersymbols, whereinthe payload sections and timing header and position prediction slotsalternate in sequence within the packet, and each timing header andposition prediction slot includes a respective timing header and arespective position prediction section which is contiguous with therespective timing header.
 14. The method as recited in claim 13, whereineach symbol consists of an up chirp and a down chirp, and eachsupersymbol consists of a concatenation of pairs of up chirps and downchirps of equal chirp lengths, the up chirps of the concatenation havingthe same up phase and the down chirps of the concatenation having thesame down phase.
 15. The method as recited in claim 14, wherein: thesupersymbols in timing headers of the timing header and positionprediction slots are phase encoded with time information indicating aduration of time for which a prediction of the position of thetransmitting platform was valid; and the supersymbols in positionprediction sections of the timing header and position prediction slotsare phase encoded with position information indicating the prediction ofthe position of the transmitting platform.
 16. The method as recited inclaim 14, wherein the up and down phases of the supersymbols in eachposition prediction section in a packet are varied from one positionprediction section to a next position prediction section to representrespective position predictions for the combined radar/communicationssystem which were valid for respective durations of the respectivecontiguous timing headers.
 17. The method as recited in claim 15,wherein the up and down phases of the supersymbols in each timing headerin a packet transmitted by a transmitting platform are varied from onetiming header to a next timing header to represent the respectivedurations of time for which the respective position predictions for thetransmitting platform were valid.
 18. The method as recited in claim 15,wherein a position prediction is associated with a timing header in eachtiming header and position prediction slot, the combined informationproviding a predicted position of the transmitting platform which wasvalid for the duration of the timing header transmission.
 19. The methodas recited in claim 13, further comprising: computing a time offset ofthe mobile platform using the timing and position information receivedfrom the at least three transmitting platforms; and adjusting a localclock onboard the mobile platform using the time offset.
 20. A systemfor determining a position of a mobile platform, comprising a mobileplatform and at least three transmitting platforms, wherein each of theat least three transmitting platforms comprises a commonradar/communications transmitter having a transmission antennaconfigured to transmit combined radar/communications waveform-modulatedsignals representing packets of data, the data in each packet includingpayload sections made up of multiple symbols and timing header andposition prediction slots made up of multiple supersymbols, wherein thepayload sections and timing header and position prediction slotsalternate in sequence within the packet, and each timing header andposition prediction slot includes a respective timing header and arespective position prediction section which is contiguous with therespective timing header, and wherein the mobile platform comprises acombined radar and communications receiver having a common receptionantenna, wherein the common radar/communications receiver is configuredto: receive timing and position information from the at least threetransmitting platforms by way of a reception antenna onboard the mobileplatform and compute a local position of the mobile platform using thetiming and position information received from the at least threetransmitting platforms, wherein the timing and position information isextracted from packets of data carried by the combinedradar/communications waveform-modulated signals received from the atleast three transmitting platforms.
 21. The system as recited in claim20, wherein each symbol consists of an up chirp and a down chirp, andeach supersymbol consists of a concatenation of pairs of up chirps anddown chirps of equal chirp lengths, the up chirps of the concatenationhaving the same up phase and the down chirps of the concatenation havingthe same down phase.
 22. The system as recited in claim 21, wherein: thesupersymbols in timing headers of the timing header and positionprediction slots are phase encoded with time information indicating aduration of time for which a prediction of the position of thetransmitting platform that transmitted the timing header and positionprediction slot was valid; and the supersymbols in position predictionsections of the timing header and position prediction slots are phaseencoded with position information indicating the prediction of theposition of the transmitting platform that transmitted the timing headerand position prediction slot.